diff --git a/Library/Homebrew/cli/args.rbi b/Library/Homebrew/cli/args.rbi
index b072016115..b719d78fa4 100644
--- a/Library/Homebrew/cli/args.rbi
+++ b/Library/Homebrew/cli/args.rbi
@@ -59,6 +59,12 @@ module Homebrew
 
       sig { returns(T.nilable(T::Boolean)) }
       def formula?; end
+
+      sig { returns(T.nilable(T::Boolean)) }
+      def zap?; end
+
+      sig { returns(T.nilable(T::Boolean)) }
+      def ignore_dependencies?; end
     end
   end
 end
diff --git a/Library/Homebrew/cli/named_args.rb b/Library/Homebrew/cli/named_args.rb
index 87663712c9..9e848f8a29 100644
--- a/Library/Homebrew/cli/named_args.rb
+++ b/Library/Homebrew/cli/named_args.rb
@@ -5,6 +5,7 @@ require "delegate"
 
 require "cask/cask_loader"
 require "cli/args"
+require "formula"
 require "formulary"
 require "keg"
 require "missing_formula"
@@ -99,6 +100,7 @@ module Homebrew
       end
       private :resolve_formula
 
+      sig { returns(T::Array[Formula]) }
       def to_resolved_formulae
         @to_resolved_formulae ||= to_formulae_and_casks(only: :formula, method: :resolve)
                                   .freeze
diff --git a/Library/Homebrew/cli/parser.rb b/Library/Homebrew/cli/parser.rb
index 331bc71416..ee00aef2b4 100644
--- a/Library/Homebrew/cli/parser.rb
+++ b/Library/Homebrew/cli/parser.rb
@@ -264,6 +264,7 @@ module Homebrew
         [remaining, non_options]
       end
 
+      sig { params(argv: T::Array[String], ignore_invalid_options: T::Boolean).returns(Args) }
       def parse(argv = ARGV.freeze, ignore_invalid_options: false)
         raise "Arguments were already parsed!" if @args_parsed
 
diff --git a/Library/Homebrew/cmd/--env.rb b/Library/Homebrew/cmd/--env.rb
index 0181ad0f3a..b8c9107e05 100644
--- a/Library/Homebrew/cmd/--env.rb
+++ b/Library/Homebrew/cmd/--env.rb
@@ -30,6 +30,7 @@ module Homebrew
     end
   end
 
+  sig { void }
   def __env
     args = __env_args.parse
 
diff --git a/Library/Homebrew/cmd/uninstall.rb b/Library/Homebrew/cmd/uninstall.rb
index bb7968a9bf..dac06da9ee 100644
--- a/Library/Homebrew/cmd/uninstall.rb
+++ b/Library/Homebrew/cmd/uninstall.rb
@@ -61,13 +61,13 @@ module Homebrew
     )
 
     if args.zap?
-      Cask::Cmd::Zap.zap_casks(
+      T.unsafe(Cask::Cmd::Zap).zap_casks(
         *casks,
         verbose: args.verbose?,
         force:   args.force?,
       )
     else
-      Cask::Cmd::Uninstall.uninstall_casks(
+      T.unsafe(Cask::Cmd::Uninstall).uninstall_casks(
         *casks,
         binaries: EnvConfig.cask_opts_binaries?,
         verbose:  args.verbose?,
diff --git a/Library/Homebrew/postinstall.rb b/Library/Homebrew/postinstall.rb
index 1c6d5df21d..6856fa07ed 100644
--- a/Library/Homebrew/postinstall.rb
+++ b/Library/Homebrew/postinstall.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: strict
 # frozen_string_literal: true
 
 old_trap = trap("INT") { exit! 130 }
@@ -17,7 +17,7 @@ begin
 
   trap("INT", old_trap)
 
-  formula = args.named.to_resolved_formulae.first
+  formula = T.must(args.named.to_resolved_formulae.first)
   formula.extend(Debrew::Formula) if args.debug?
   formula.run_post_install
 rescue Exception => e # rubocop:disable Lint/RescueException
diff --git a/Library/Homebrew/sorbet/rbi/upstream.rbi b/Library/Homebrew/sorbet/rbi/upstream.rbi
index 4a77637e5a..d36710b7e2 100644
--- a/Library/Homebrew/sorbet/rbi/upstream.rbi
+++ b/Library/Homebrew/sorbet/rbi/upstream.rbi
@@ -1,13 +1,16 @@
 # typed: strict
 
-class Pathname
-  # https://github.com/sorbet/sorbet/pull/3676
-  sig { params(p1: T.any(String, Pathname), p2: String).returns(T::Array[Pathname]) }
-  def self.glob(p1, p2 = T.unsafe(nil)); end
-
-  # https://github.com/sorbet/sorbet/pull/3678
-  sig { params(with_directory: T::Boolean).returns(T::Array[Pathname]) }
-  def children(with_directory = true); end
+class IO
+  # https://github.com/sorbet/sorbet/pull/3722
+  sig do
+    type_parameters(:U).params(
+      fd: T.any(String, Integer),
+      mode: T.any(Integer, String),
+      opt: T.nilable(T::Hash[Symbol, T.untyped]),
+      blk: T.proc.params(io: T.attached_class).returns(T.type_parameter(:U))
+    ).returns(T.type_parameter(:U))
+  end
+  def self.open(fd, mode='r', opt=nil, &blk); end
 end
 
 module FileUtils