diff --git a/Library/Homebrew/cmd/--cache.rb b/Library/Homebrew/cmd/--cache.rb
index 1e39aa66c9..00d0847748 100644
--- a/Library/Homebrew/cmd/--cache.rb
+++ b/Library/Homebrew/cmd/--cache.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "fetch"
@@ -10,10 +10,8 @@ module Homebrew
 
   extend Fetch
 
-  module_function
-
   sig { returns(CLI::Parser) }
-  def __cache_args
+  def self.__cache_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         Display Homebrew's download cache. See also `HOMEBREW_CACHE`.
@@ -41,7 +39,7 @@ module Homebrew
   end
 
   sig { void }
-  def __cache
+  def self.__cache
     args = __cache_args.parse
 
     if args.no_named?
@@ -61,9 +59,9 @@ module Homebrew
   end
 
   sig { params(formula: Formula, args: CLI::Args).void }
-  def print_formula_cache(formula, args:)
+  def self.print_formula_cache(formula, args:)
     if fetch_bottle?(formula, args: args)
-      puts formula.bottle_for_tag(args.bottle_tag&.to_sym).cached_download
+      puts formula.bottle_for_tag(args.bottle_tag&.to_sym)&.cached_download
     elsif args.HEAD?
       puts formula.head.cached_download
     else
@@ -72,7 +70,7 @@ module Homebrew
   end
 
   sig { params(cask: Cask::Cask).void }
-  def print_cask_cache(cask)
+  def self.print_cask_cache(cask)
     puts Cask::Download.new(cask).downloader.cached_location
   end
 end
diff --git a/Library/Homebrew/cmd/--prefix.rb b/Library/Homebrew/cmd/--prefix.rb
index e6c476466a..ead995cb62 100644
--- a/Library/Homebrew/cmd/--prefix.rb
+++ b/Library/Homebrew/cmd/--prefix.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "cli/parser"
@@ -105,7 +105,8 @@ module Homebrew
     arguments.concat UNBREWED_EXCLUDE_PATHS.flat_map { |d| %W[! -path #{d}] }
     arguments.push ")"
 
-    cd HOMEBREW_PREFIX
+    # This is a false positive type error: https://github.com/sorbet/sorbet/issues/6812
+    T.unsafe(self).cd HOMEBREW_PREFIX
     safe_system "find", *arguments
   end
 end
diff --git a/Library/Homebrew/cmd/commands.rb b/Library/Homebrew/cmd/commands.rb
index ea41c1efa3..f7ea8186b4 100644
--- a/Library/Homebrew/cmd/commands.rb
+++ b/Library/Homebrew/cmd/commands.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "cli/parser"
@@ -32,7 +32,7 @@ module Homebrew
       return
     end
 
-    prepend_separator = false
+    prepend_separator = T.let(false, T::Boolean)
 
     {
       "Built-in commands"           => Commands.internal_commands,
diff --git a/Library/Homebrew/cmd/deps.rb b/Library/Homebrew/cmd/deps.rb
index 2ca0ca80bc..f04add7c65 100644
--- a/Library/Homebrew/cmd/deps.rb
+++ b/Library/Homebrew/cmd/deps.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "formula"
@@ -12,10 +12,8 @@ module Homebrew
 
   extend DependenciesHelpers
 
-  module_function
-
   sig { returns(CLI::Parser) }
-  def deps_args
+  def self.deps_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         Show dependencies for <formula>. Additional options specific to <formula>
@@ -78,7 +76,7 @@ module Homebrew
     end
   end
 
-  def deps
+  def self.deps
     args = deps_args.parse
 
     all = args.eval_all?
@@ -164,16 +162,16 @@ module Homebrew
     puts all_deps
   end
 
-  def sorted_dependents(formulae_or_casks)
+  def self.sorted_dependents(formulae_or_casks)
     dependents(formulae_or_casks).sort_by(&:name)
   end
 
-  def condense_requirements(deps, args:)
+  def self.condense_requirements(deps, args:)
     deps.select! { |dep| dep.is_a?(Dependency) } unless args.include_requirements?
     deps.select! { |dep| dep.is_a?(Requirement) || dep.installed? } if args.installed?
   end
 
-  def dep_display_name(dep, args:)
+  def self.dep_display_name(dep, args:)
     str = if dep.is_a? Requirement
       if args.include_requirements?
         ":#{dep.display_s}"
@@ -198,7 +196,7 @@ module Homebrew
     str
   end
 
-  def deps_for_dependent(d, args:, recursive: false)
+  def self.deps_for_dependent(d, args:, recursive: false)
     includes, ignores = args_includes_ignores(args)
 
     deps = d.runtime_dependencies if @use_runtime_dependencies
@@ -214,11 +212,11 @@ module Homebrew
     deps + reqs.to_a
   end
 
-  def deps_for_dependents(dependents, args:, recursive: false, &block)
+  def self.deps_for_dependents(dependents, args:, recursive: false, &block)
     dependents.map { |d| deps_for_dependent(d, recursive: recursive, args: args) }.reduce(&block)
   end
 
-  def puts_deps(dependents, args:, recursive: false)
+  def self.puts_deps(dependents, args:, recursive: false)
     dependents.each do |dependent|
       deps = deps_for_dependent(dependent, recursive: recursive, args: args)
       condense_requirements(deps, args: args)
@@ -228,7 +226,7 @@ module Homebrew
     end
   end
 
-  def dot_code(dependents, recursive:, args:)
+  def self.dot_code(dependents, recursive:, args:)
     dep_graph = {}
     dependents.each do |d|
       graph_deps(d, dep_graph: dep_graph, recursive: recursive, args: args)
@@ -251,7 +249,7 @@ module Homebrew
     "digraph {\n#{dot_code}\n}"
   end
 
-  def graph_deps(f, dep_graph:, recursive:, args:)
+  def self.graph_deps(f, dep_graph:, recursive:, args:)
     return if dep_graph.key?(f)
 
     dependables = dependables(f, args: args)
@@ -268,7 +266,7 @@ module Homebrew
     end
   end
 
-  def puts_deps_tree(dependents, args:, recursive: false)
+  def self.puts_deps_tree(dependents, args:, recursive: false)
     dependents.each do |d|
       puts d.full_name
       recursive_deps_tree(d, dep_stack: [], prefix: "", recursive: recursive, args: args)
@@ -276,7 +274,7 @@ module Homebrew
     end
   end
 
-  def dependables(f, args:)
+  def self.dependables(f, args:)
     includes, ignores = args_includes_ignores(args)
     deps = @use_runtime_dependencies ? f.runtime_dependencies : f.deps
     deps = reject_ignores(deps, ignores, includes)
@@ -285,7 +283,7 @@ module Homebrew
     reqs + deps
   end
 
-  def recursive_deps_tree(f, dep_stack:, prefix:, recursive:, args:)
+  def self.recursive_deps_tree(f, dep_stack:, prefix:, recursive:, args:)
     dependables = dependables(f, args: args)
     max = dependables.length - 1
     dep_stack.push f.name
diff --git a/Library/Homebrew/cmd/desc.rb b/Library/Homebrew/cmd/desc.rb
index 965e8f23a8..8abbf08588 100644
--- a/Library/Homebrew/cmd/desc.rb
+++ b/Library/Homebrew/cmd/desc.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "descriptions"
diff --git a/Library/Homebrew/cmd/doctor.rb b/Library/Homebrew/cmd/doctor.rb
index 8f4de98b8c..d5956b2242 100644
--- a/Library/Homebrew/cmd/doctor.rb
+++ b/Library/Homebrew/cmd/doctor.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "diagnostic"
@@ -8,10 +8,8 @@ require "cask/caskroom"
 module Homebrew
   extend T::Sig
 
-  module_function
-
   sig { returns(CLI::Parser) }
-  def doctor_args
+  def self.doctor_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         Check your system for potential problems. Will exit with a non-zero status
@@ -30,7 +28,7 @@ module Homebrew
     end
   end
 
-  def doctor
+  def self.doctor
     args = doctor_args.parse
 
     inject_dump_stats!(Diagnostic::Checks, /^check_*/) if args.audit_debug?
@@ -53,7 +51,7 @@ module Homebrew
       methods = args.named
     end
 
-    first_warning = true
+    first_warning = T.let(true, T::Boolean)
     methods.each do |method|
       $stderr.puts Formatter.headline("Checking #{method}", color: :magenta) if args.debug?
       unless checks.respond_to?(method)
diff --git a/Library/Homebrew/cmd/fetch.rb b/Library/Homebrew/cmd/fetch.rb
index d348b69bf2..24234c7150 100644
--- a/Library/Homebrew/cmd/fetch.rb
+++ b/Library/Homebrew/cmd/fetch.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "formula"
@@ -11,12 +11,10 @@ module Homebrew
 
   extend Fetch
 
-  module_function
-
   FETCH_MAX_TRIES = 5
 
   sig { returns(CLI::Parser) }
-  def fetch_args
+  def self.fetch_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         Download a bottle (if available) or source packages for <formula>e
@@ -65,7 +63,7 @@ module Homebrew
     end
   end
 
-  def fetch
+  def self.fetch
     args = fetch_args.parse
 
     bucket = if args.deps?
@@ -132,7 +130,7 @@ module Homebrew
     end
   end
 
-  def fetch_resource(r, args:)
+  def self.fetch_resource(r, args:)
     puts "Resource: #{r.name}"
     fetch_fetchable r, args: args
   rescue ChecksumMismatchError => e
@@ -140,28 +138,28 @@ module Homebrew
     opoo "Resource #{r.name} reports different sha256: #{e.expected}"
   end
 
-  def fetch_formula(f, args:)
+  def self.fetch_formula(f, args:)
     fetch_fetchable f, args: args
   rescue ChecksumMismatchError => e
     retry if retry_fetch?(f, args: args)
     opoo "Formula reports different sha256: #{e.expected}"
   end
 
-  def fetch_cask(cask_download, args:)
+  def self.fetch_cask(cask_download, args:)
     fetch_fetchable cask_download, args: args
   rescue ChecksumMismatchError => e
     retry if retry_fetch?(cask_download, args: args)
     opoo "Cask reports different sha256: #{e.expected}"
   end
 
-  def fetch_patch(p, args:)
+  def self.fetch_patch(p, args:)
     fetch_fetchable p, args: args
   rescue ChecksumMismatchError => e
     opoo "Patch reports different sha256: #{e.expected}"
     Homebrew.failed = true
   end
 
-  def retry_fetch?(f, args:)
+  def self.retry_fetch?(f, args:)
     @fetch_tries ||= Hash.new { |h, k| h[k] = 1 }
     if args.retry? && (@fetch_tries[f] < FETCH_MAX_TRIES)
       wait = 2 ** @fetch_tries[f]
@@ -180,7 +178,7 @@ module Homebrew
     end
   end
 
-  def fetch_fetchable(f, args:)
+  def self.fetch_fetchable(f, args:)
     f.clear_cache if args.force?
 
     already_fetched = f.cached_download.exist?
diff --git a/Library/Homebrew/cmd/info.rb b/Library/Homebrew/cmd/info.rb
index 1a4d3f3b42..82d5de39c4 100644
--- a/Library/Homebrew/cmd/info.rb
+++ b/Library/Homebrew/cmd/info.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "missing_formula"
@@ -191,7 +191,7 @@ module Homebrew
     version_hash[version]
   end
 
-  sig { params(all: T::Boolean, args: CLI::Args).void }
+  sig { params(all: T::Boolean, args: T.untyped).void }
   def print_json(all, args:)
     raise FormulaOrCaskUnspecifiedError if !(all || args.installed?) && args.no_named?
 
diff --git a/Library/Homebrew/cmd/install.rb b/Library/Homebrew/cmd/install.rb
index 886631f820..7481ddb3d0 100644
--- a/Library/Homebrew/cmd/install.rb
+++ b/Library/Homebrew/cmd/install.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "cask/config"
@@ -279,7 +279,11 @@ module Homebrew
     Homebrew.failed = true
 
     # formula name or cask token
-    name = e.try(:name) || e.token
+    name = case e
+    when FormulaOrCaskUnavailableError then e.name
+    when Cask::CaskUnavailableError then e.token
+    else T.absurd(e)
+    end
 
     if name == "updog"
       ofail "What's updog?"
diff --git a/Library/Homebrew/cmd/list.rb b/Library/Homebrew/cmd/list.rb
index 2bab5bd361..2a5ee074cb 100644
--- a/Library/Homebrew/cmd/list.rb
+++ b/Library/Homebrew/cmd/list.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "metafiles"
diff --git a/Library/Homebrew/cmd/log.rb b/Library/Homebrew/cmd/log.rb
index 9602e87d7c..5b84bcd774 100644
--- a/Library/Homebrew/cmd/log.rb
+++ b/Library/Homebrew/cmd/log.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "cli/parser"
@@ -54,7 +54,8 @@ module Homebrew
   end
 
   def git_log(cd_dir, path = nil, tap = nil, args:)
-    cd cd_dir
+    # This is a false positive type error: https://github.com/sorbet/sorbet/issues/6812
+    T.unsafe(self).cd cd_dir
     repo = Utils.popen_read("git", "rev-parse", "--show-toplevel").chomp
     if tap
       name = tap.to_s
diff --git a/Library/Homebrew/cmd/options.rb b/Library/Homebrew/cmd/options.rb
index d83f825529..8263c1cac3 100644
--- a/Library/Homebrew/cmd/options.rb
+++ b/Library/Homebrew/cmd/options.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "formula"
diff --git a/Library/Homebrew/cmd/outdated.rb b/Library/Homebrew/cmd/outdated.rb
index 28186cce9a..becc267a2d 100644
--- a/Library/Homebrew/cmd/outdated.rb
+++ b/Library/Homebrew/cmd/outdated.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "formula"
@@ -11,10 +11,8 @@ require "api"
 module Homebrew
   extend T::Sig
 
-  module_function
-
   sig { returns(CLI::Parser) }
-  def outdated_args
+  def self.outdated_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         List installed casks and formulae that have an updated version available. By default, version
@@ -52,7 +50,7 @@ module Homebrew
     end
   end
 
-  def outdated
+  def self.outdated
     args = outdated_args.parse
 
     case json_version(args.json)
@@ -90,7 +88,7 @@ module Homebrew
     Homebrew.failed = args.named.present? && outdated.present?
   end
 
-  def print_outdated(formulae_or_casks, args:)
+  def self.print_outdated(formulae_or_casks, args:)
     formulae_or_casks.each do |formula_or_cask|
       if formula_or_cask.is_a?(Formula)
         f = formula_or_cask
@@ -128,7 +126,7 @@ module Homebrew
     end
   end
 
-  def json_info(formulae_or_casks, args:)
+  def self.json_info(formulae_or_casks, args:)
     formulae_or_casks.map do |formula_or_cask|
       if formula_or_cask.is_a?(Formula)
         f = formula_or_cask
@@ -153,11 +151,11 @@ module Homebrew
     end
   end
 
-  def verbose?
+  def self.verbose?
     ($stdout.tty? || super) && !quiet?
   end
 
-  def json_version(version)
+  def self.json_version(version)
     version_hash = {
       nil  => nil,
       true => :default,
@@ -170,11 +168,11 @@ module Homebrew
     version_hash[version]
   end
 
-  def outdated_formulae(args:)
+  def self.outdated_formulae(args:)
     select_outdated((args.named.to_resolved_formulae.presence || Formula.installed), args: args).sort
   end
 
-  def outdated_casks(args:)
+  def self.outdated_casks(args:)
     if args.named.present?
       select_outdated(args.named.to_casks, args: args)
     else
@@ -182,7 +180,7 @@ module Homebrew
     end
   end
 
-  def outdated_formulae_casks(args:)
+  def self.outdated_formulae_casks(args:)
     formulae, casks = args.named.to_resolved_formulae_to_casks
 
     if formulae.blank? && casks.blank?
@@ -193,7 +191,7 @@ module Homebrew
     [select_outdated(formulae, args: args).sort, select_outdated(casks, args: args)]
   end
 
-  def select_outdated(formulae_or_casks, args:)
+  def self.select_outdated(formulae_or_casks, args:)
     formulae_or_casks.select do |formula_or_cask|
       if formula_or_cask.is_a?(Formula)
         formula_or_cask.outdated?(fetch_head: args.fetch_HEAD?)
diff --git a/Library/Homebrew/cmd/reinstall.rb b/Library/Homebrew/cmd/reinstall.rb
index 1a61d57534..8eeb2f370c 100644
--- a/Library/Homebrew/cmd/reinstall.rb
+++ b/Library/Homebrew/cmd/reinstall.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "formula_installer"
diff --git a/Library/Homebrew/cmd/search.rb b/Library/Homebrew/cmd/search.rb
index 191ae105f9..c666b7df65 100644
--- a/Library/Homebrew/cmd/search.rb
+++ b/Library/Homebrew/cmd/search.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "formula"
diff --git a/Library/Homebrew/cmd/tap-info.rb b/Library/Homebrew/cmd/tap-info.rb
index 4a471a8e01..039c861dca 100644
--- a/Library/Homebrew/cmd/tap-info.rb
+++ b/Library/Homebrew/cmd/tap-info.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "cli/parser"
@@ -64,6 +64,7 @@ module Homebrew
       info += ", #{Tap::TAP_DIRECTORY.dup.abv}" if Tap::TAP_DIRECTORY.directory?
       puts info
     else
+      info = ""
       taps.each_with_index do |tap, i|
         puts unless i.zero?
         info = "#{tap}: "
diff --git a/Library/Homebrew/cmd/upgrade.rb b/Library/Homebrew/cmd/upgrade.rb
index 94323b369f..58a220cf52 100644
--- a/Library/Homebrew/cmd/upgrade.rb
+++ b/Library/Homebrew/cmd/upgrade.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "cli/parser"
@@ -121,7 +121,7 @@ module Homebrew
     Homebrew.messages.display_messages(display_times: args.display_times?)
   end
 
-  sig { params(formulae: T::Array[Formula], args: CLI::Args).returns(T::Boolean) }
+  sig { params(formulae: T::Array[Formula], args: T.untyped).returns(T::Boolean) }
   def upgrade_outdated_formulae(formulae, args:)
     return false if args.cask?
 
@@ -226,7 +226,7 @@ module Homebrew
     true
   end
 
-  sig { params(casks: T::Array[Cask::Cask], args: CLI::Args).returns(T::Boolean) }
+  sig { params(casks: T::Array[Cask::Cask], args: T.untyped).returns(T::Boolean) }
   def upgrade_outdated_casks(casks, args:)
     return false if args.formula?
 
diff --git a/Library/Homebrew/cmd/uses.rb b/Library/Homebrew/cmd/uses.rb
index e1d0c8830c..a4620bc159 100644
--- a/Library/Homebrew/cmd/uses.rb
+++ b/Library/Homebrew/cmd/uses.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 # `brew uses foo bar` returns formulae that use both foo and bar
@@ -15,10 +15,8 @@ module Homebrew
 
   extend DependenciesHelpers
 
-  module_function
-
   sig { returns(CLI::Parser) }
-  def uses_args
+  def self.uses_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         Show formulae and casks that specify <formula> as a dependency; that is, show dependents
@@ -55,7 +53,7 @@ module Homebrew
     end
   end
 
-  def uses
+  def self.uses
     args = uses_args.parse
 
     Formulary.enable_factory_cache!
@@ -88,7 +86,7 @@ module Homebrew
     odie "Missing formulae should not have dependents!" if used_formulae_missing
   end
 
-  def intersection_of_dependents(use_runtime_dependents, used_formulae, args:)
+  def self.intersection_of_dependents(use_runtime_dependents, used_formulae, args:)
     recursive = args.recursive?
     show_formulae_and_casks = !args.formula? && !args.cask?
     includes, ignores = args_includes_ignores(args)
@@ -132,7 +130,7 @@ module Homebrew
     end
   end
 
-  def select_used_dependents(dependents, used_formulae, recursive, includes, ignores)
+  def self.select_used_dependents(dependents, used_formulae, recursive, includes, ignores)
     dependents.select do |d|
       deps = if recursive
         recursive_includes(Dependency, d, includes, ignores)
diff --git a/Library/Homebrew/dev-cmd/bump-formula-pr.rb b/Library/Homebrew/dev-cmd/bump-formula-pr.rb
index b72ecd2ac1..2d480cc0bf 100644
--- a/Library/Homebrew/dev-cmd/bump-formula-pr.rb
+++ b/Library/Homebrew/dev-cmd/bump-formula-pr.rb
@@ -172,7 +172,7 @@ module Homebrew
           EOS
         end
         check_new_version(formula, tap_remote_repo, url: old_url, tag: new_tag, args: args) if new_version.blank?
-        resource_path, forced_version = fetch_resource(formula, new_version, old_url, tag: new_tag)
+        resource_path, forced_version = fetch_resource_and_forced_version(formula, new_version, old_url, tag: new_tag)
         new_revision = Utils.popen_read("git", "-C", resource_path.to_s, "rev-parse", "-q", "--verify", "HEAD")
         new_revision = new_revision.strip
       elsif new_revision.blank?
@@ -199,7 +199,7 @@ module Homebrew
         EOS
       end
       check_new_version(formula, tap_remote_repo, url: new_url, args: args) if new_version.blank?
-      resource_path, forced_version = fetch_resource(formula, new_version, new_url)
+      resource_path, forced_version = fetch_resource_and_forced_version(formula, new_version, new_url)
       Utils::Tar.validate_file(resource_path)
       new_hash = resource_path.sha256
     end
@@ -388,7 +388,7 @@ module Homebrew
     end
   end
 
-  def fetch_resource(formula, new_version, url, **specs)
+  def fetch_resource_and_forced_version(formula, new_version, url, **specs)
     resource = Resource.new
     resource.url(url, specs)
     resource.owner = Resource.new(formula.name)
diff --git a/Library/Homebrew/utils.rb b/Library/Homebrew/utils.rb
index 3ca0e63535..c0eaae9b41 100644
--- a/Library/Homebrew/utils.rb
+++ b/Library/Homebrew/utils.rb
@@ -26,9 +26,7 @@ module Homebrew
   extend Context
   extend T::Sig
 
-  module_function
-
-  def _system(cmd, *args, **options)
+  def self._system(cmd, *args, **options)
     pid = fork do
       yield if block_given?
       args.map!(&:to_s)
@@ -43,7 +41,7 @@ module Homebrew
     $CHILD_STATUS.success?
   end
 
-  def system(cmd, *args, **options)
+  def self.system(cmd, *args, **options)
     if verbose?
       puts "#{cmd} #{args * " "}".gsub(RUBY_PATH, "ruby")
                                  .gsub($LOAD_PATH.join(File::PATH_SEPARATOR).to_s, "$LOAD_PATH")
@@ -53,7 +51,7 @@ module Homebrew
 
   # rubocop:disable Style/GlobalVars
   sig { params(the_module: Module, pattern: Regexp).void }
-  def inject_dump_stats!(the_module, pattern)
+  def self.inject_dump_stats!(the_module, pattern)
     @injected_dump_stat_modules ||= {}
     @injected_dump_stat_modules[the_module] ||= []
     injected_methods = @injected_dump_stat_modules[the_module]