diff --git a/Library/Homebrew/api/cask.rb b/Library/Homebrew/api/cask.rb
index 5de578f0ed..df336931a9 100644
--- a/Library/Homebrew/api/cask.rb
+++ b/Library/Homebrew/api/cask.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cachable"
@@ -21,7 +21,7 @@ module Homebrew
 
       private_class_method :cache
 
-      sig { params(token: String).returns(Hash) }
+      sig { params(token: String).returns(T::Hash[String, T.untyped]) }
       def self.fetch(token)
         Homebrew::API.fetch "cask/#{token}.json"
       end
@@ -47,6 +47,7 @@ module Homebrew
                                           .load(config: cask.config)
       end
 
+      sig { returns(Pathname) }
       def self.cached_json_file_path
         HOMEBREW_CACHE_API/api_filename
       end
@@ -70,7 +71,7 @@ module Homebrew
       end
       private_class_method :download_and_cache_data!
 
-      sig { returns(T::Hash[String, Hash]) }
+      sig { returns(T::Hash[String, T::Hash[String, T.untyped]]) }
       def self.all_casks
         unless cache.key?("casks")
           json_updated = download_and_cache_data!
diff --git a/Library/Homebrew/cask/artifact_set.rb b/Library/Homebrew/cask/artifact_set.rb
index 517debcd25..8f1da460b4 100644
--- a/Library/Homebrew/cask/artifact_set.rb
+++ b/Library/Homebrew/cask/artifact_set.rb
@@ -1,9 +1,14 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 module Cask
   # Sorted set containing all cask artifacts.
   class ArtifactSet < ::Set
+    extend T::Generic
+
+    Elem = type_member(:out) { { fixed: Artifact::AbstractArtifact } }
+
+    sig { params(block: T.nilable(T.proc.params(arg0: Elem).returns(T.untyped))).void }
     def each(&block)
       return enum_for(T.must(__method__)) { size } unless block
 
@@ -11,6 +16,7 @@ module Cask
       self
     end
 
+    sig { returns(T::Array[Artifact::AbstractArtifact]) }
     def to_a
       super.sort
     end
diff --git a/Library/Homebrew/cask/cask_loader.rb b/Library/Homebrew/cask/cask_loader.rb
index 24befa53a3..4dd39bfc0f 100644
--- a/Library/Homebrew/cask/cask_loader.rb
+++ b/Library/Homebrew/cask/cask_loader.rb
@@ -295,7 +295,7 @@ module Cask
       sig { returns(Pathname) }
       attr_reader :path
 
-      sig { returns(T.nilable(T::Hash[T.any(String, Symbol), T.anything])) }
+      sig { returns(T.nilable(T::Hash[String, T.untyped])) }
       attr_reader :from_json
 
       sig {
@@ -320,7 +320,7 @@ module Cask
       sig {
         params(
           token:     String,
-          from_json: T.nilable(T::Hash[T.any(String, Symbol), T.anything]),
+          from_json: T.nilable(T::Hash[String, T.untyped]),
           path:      T.nilable(Pathname),
         ).void
       }
diff --git a/Library/Homebrew/cask/installer.rb b/Library/Homebrew/cask/installer.rb
index 9cc482012a..7819d4089a 100644
--- a/Library/Homebrew/cask/installer.rb
+++ b/Library/Homebrew/cask/installer.rb
@@ -304,6 +304,20 @@ on_request: true)
 
         next if artifact.is_a?(Artifact::Binary) && !binaries?
 
+        artifact = T.cast(
+          artifact,
+          T.any(
+            Artifact::AbstractFlightBlock,
+            Artifact::Installer,
+            Artifact::KeyboardLayout,
+            Artifact::Mdimporter,
+            Artifact::Moved,
+            Artifact::Pkg,
+            Artifact::Qlplugin,
+            Artifact::Symlinked,
+          ),
+        )
+
         artifact.install_phase(
           command: @command, verbose: verbose?, adopt: adopt?, auto_updates: @cask.auto_updates,
           force: force?, predecessor:
@@ -549,6 +563,18 @@ on_request: true)
 
       artifacts.each do |artifact|
         if artifact.respond_to?(:uninstall_phase)
+          artifact = T.cast(
+            artifact,
+            T.any(
+              Artifact::AbstractFlightBlock,
+              Artifact::KeyboardLayout,
+              Artifact::Moved,
+              Artifact::Qlplugin,
+              Artifact::Symlinked,
+              Artifact::Uninstall,
+            ),
+          )
+
           odebug "Uninstalling artifact of class #{artifact.class}"
           artifact.uninstall_phase(
             command:   @command,
@@ -563,6 +589,8 @@ on_request: true)
 
         next unless artifact.respond_to?(:post_uninstall_phase)
 
+        artifact = T.cast(artifact, Artifact::Uninstall)
+
         odebug "Post-uninstalling artifact of class #{artifact.class}"
         artifact.post_uninstall_phase(
           command:   @command,