diff --git a/Library/Homebrew/build.rb b/Library/Homebrew/build.rb
index adebc41e33..702517fd03 100644
--- a/Library/Homebrew/build.rb
+++ b/Library/Homebrew/build.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 # This script is loaded by formula_installer as a separate instance.
@@ -23,28 +23,40 @@ require "extend/pathname/write_mkpath_extension"
 class Build
   include Utils::Output::Mixin
 
-  attr_reader :formula, :deps, :reqs, :args
+  sig { returns(Formula) }
+  attr_reader :formula
 
+  sig { returns(T::Array[Dependency]) }
+  attr_reader :deps
+
+  sig { returns(Requirements) }
+  attr_reader :reqs
+
+  sig { returns(Homebrew::Cmd::InstallCmd::Args) }
+  attr_reader :args
+
+  sig { params(formula: Formula, options: Options, args: Homebrew::Cmd::InstallCmd::Args).void }
   def initialize(formula, options, args:)
     @formula = formula
     @formula.build = BuildOptions.new(options, formula.options)
-    @args = args
+    @args = T.let(args, Homebrew::Cmd::InstallCmd::Args)
+    @deps = T.let([], T::Array[Dependency])
+    @reqs = T.let(Requirements.new, Requirements)
 
-    if args.ignore_dependencies?
-      @deps = []
-      @reqs = []
-    else
-      @deps = expand_deps
-      @reqs = expand_reqs
-    end
+    return if args.ignore_dependencies?
+
+    @deps = expand_deps
+    @reqs = expand_reqs
   end
 
+  sig { params(dependent: Formula).returns(BuildOptions) }
   def effective_build_options_for(dependent)
     args  = dependent.build.used_options
     args |= Tab.for_formula(dependent).used_options
     BuildOptions.new(args, dependent.options)
   end
 
+  sig { returns(Requirements) }
   def expand_reqs
     formula.recursive_requirements do |dependent, req|
       build = effective_build_options_for(dependent)
@@ -54,6 +66,7 @@ class Build
     end
   end
 
+  sig { returns(T::Array[Dependency]) }
   def expand_deps
     formula.recursive_dependencies do |dependent, dep|
       build = effective_build_options_for(dependent)
@@ -67,6 +80,7 @@ class Build
     end
   end
 
+  sig { void }
   def install
     formula_deps = deps.map(&:to_formula)
     keg_only_deps = formula_deps.select(&:keg_only?)
@@ -79,7 +93,7 @@ class Build
     ENV.activate_extensions!(env: args.env)
 
     if superenv?(args.env)
-      superenv = T.cast(ENV, Superenv)
+      superenv = ENV
       superenv.keg_only_deps = keg_only_deps
       superenv.deps = formula_deps
       superenv.run_time_deps = run_time_deps
@@ -192,7 +206,7 @@ class Build
             tab.write
 
             # Find and link metafiles
-            formula.prefix.install_metafiles formula.buildpath
+            formula.prefix.install_metafiles T.must(formula.buildpath)
             formula.prefix.install_metafiles formula.libexec if formula.libexec.exist?
 
             normalize_pod2man_outputs!(formula)
@@ -202,6 +216,7 @@ class Build
     end
   end
 
+  sig { returns(T::Array[Symbol]) }
   def detect_stdlibs
     keg = Keg.new(formula.prefix)
 
@@ -211,13 +226,15 @@ class Build
     keg.detect_cxx_stdlibs(skip_executables: true)
   end
 
+  sig { params(formula: Formula).void }
   def fixopt(formula)
     path = if formula.linked_keg.directory? && formula.linked_keg.symlink?
       formula.linked_keg.resolved_path
     elsif formula.prefix.directory?
       formula.prefix
-    elsif (kids = formula.rack.children).size == 1 && kids.first.directory?
-      kids.first
+    elsif (children = formula.rack.children.presence) && children.size == 1 &&
+          (first_child = children.first.presence) && first_child.directory?
+      first_child
     else
       raise
     end
@@ -226,6 +243,7 @@ class Build
     raise "#{formula.opt_prefix} not present or broken\nPlease reinstall #{formula.full_name}. Sorry :("
   end
 
+  sig { params(formula: Formula).void }
   def normalize_pod2man_outputs!(formula)
     keg = Keg.new(formula.prefix)
     keg.normalize_pod2man_outputs!
@@ -245,7 +263,7 @@ begin
 
   trap("INT", old_trap)
 
-  formula = args.named.to_formulae.first
+  formula = args.named.to_formulae.fetch(0)
   options = Options.create(args.flags_only)
   build   = Build.new(formula, options, args:)
 
diff --git a/Library/Homebrew/build_environment.rb b/Library/Homebrew/build_environment.rb
index 48eac54ff6..2faca110d6 100644
--- a/Library/Homebrew/build_environment.rb
+++ b/Library/Homebrew/build_environment.rb
@@ -1,11 +1,11 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 # Settings for the build environment.
 class BuildEnvironment
   sig { params(settings: Symbol).void }
   def initialize(*settings)
-    @settings = Set.new(settings)
+    @settings = T.let(Set.new(settings), T::Set[Symbol])
   end
 
   sig { params(args: T::Enumerable[Symbol]).returns(T.self_type) }
@@ -29,16 +29,17 @@ class BuildEnvironment
   module DSL
     # Initialise @env for each class which may use this DSL (e.g. each formula subclass).
     # `env` may never be called and it needs to be initialised before the class is frozen.
+    sig { params(child: T.untyped).void }
     def inherited(child)
       super
       child.instance_eval do
-        @env = BuildEnvironment.new
+        @env = T.let(BuildEnvironment.new, T.nilable(BuildEnvironment))
       end
     end
 
     sig { params(settings: Symbol).returns(BuildEnvironment) }
     def env(*settings)
-      @env.merge(settings)
+      T.must(@env).merge(settings)
     end
   end
 
diff --git a/Library/Homebrew/build_options.rb b/Library/Homebrew/build_options.rb
index 3dff77598f..d6b4c94c16 100644
--- a/Library/Homebrew/build_options.rb
+++ b/Library/Homebrew/build_options.rb
@@ -1,11 +1,12 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 # Options for a formula build.
 class BuildOptions
+  sig { params(args: Options, options: Options).void }
   def initialize(args, options)
-    @args = args
-    @options = options
+    @args = T.let(args, Options)
+    @options = T.let(options, Options)
   end
 
   # True if a {Formula} is being built with a specific option.
@@ -29,8 +30,13 @@ class BuildOptions
   #   args << "--with-example1"
   # end
   # ```
+  sig { params(val: T.any(String, Requirement, Dependency)).returns(T::Boolean) }
   def with?(val)
-    option_names = val.respond_to?(:option_names) ? val.option_names : [val]
+    option_names = if val.is_a?(String)
+      [val]
+    else
+      val.option_names
+    end
 
     option_names.any? do |name|
       if option_defined? "with-#{name}"
@@ -50,11 +56,13 @@ class BuildOptions
   # ```ruby
   # args << "--no-spam-plz" if build.without? "spam"
   # ```
+  sig { params(val: T.any(String, Requirement, Dependency)).returns(T::Boolean) }
   def without?(val)
     !with?(val)
   end
 
   # True if a {Formula} is being built as a bottle (i.e. binary package).
+  sig { returns(T::Boolean) }
   def bottle?
     include? "build-bottle"
   end
@@ -75,6 +83,7 @@ class BuildOptions
   #   args << "--and-a-cold-beer" if build.with? "cold-beer"
   # end
   # ```
+  sig { returns(T::Boolean) }
   def head?
     include? "HEAD"
   end
@@ -87,29 +96,35 @@ class BuildOptions
   # ```ruby
   # args << "--some-feature" if build.stable?
   # ```
+  sig { returns(T::Boolean) }
   def stable?
     !head?
   end
 
   # True if the build has any arguments or options specified.
+  sig { returns(T::Boolean) }
   def any_args_or_options?
     !@args.empty? || !@options.empty?
   end
 
+  sig { returns(Options) }
   def used_options
     @options & @args
   end
 
+  sig { returns(Options) }
   def unused_options
     @options - @args
   end
 
   private
 
+  sig { params(name: String).returns(T::Boolean) }
   def include?(name)
     @args.include?("--#{name}")
   end
 
+  sig { params(name: String).returns(T::Boolean) }
   def option_defined?(name)
     @options.include? name
   end