diff --git a/Library/Homebrew/download_strategy.rb b/Library/Homebrew/download_strategy.rb
index 0074b62ec7..cd57614bd1 100644
--- a/Library/Homebrew/download_strategy.rb
+++ b/Library/Homebrew/download_strategy.rb
@@ -463,15 +463,10 @@ class CurlDownloadStrategy < AbstractFileDownloadStrategy
       url = url.sub(%r{^https?://#{GitHubPackages::URL_DOMAIN}/}o, "#{domain.chomp("/")}/")
     end
 
-    output, _, _status = curl_output(
-      "--location", "--silent", "--head", "--request", "GET", url.to_s,
-      timeout: timeout
-    )
-    parsed_output = parse_curl_output(output)
+    parsed_output = curl_head(url.to_s, timeout: timeout)
+    parsed_headers = parsed_output.fetch(:responses).map { |r| r.fetch(:headers) }
 
-    lines = output.to_s.lines.map(&:chomp)
-
-    final_url = curl_response_follow_redirections(parsed_output[:responses], url)
+    final_url = curl_response_follow_redirections(parsed_output.fetch(:responses), url)
 
     content_disposition_parser = Mechanize::HTTP::ContentDispositionParser.new
 
@@ -500,19 +495,20 @@ class CurlDownloadStrategy < AbstractFileDownloadStrategy
       File.basename(filename)
     end
 
-    filenames = lines.map(&parse_content_disposition).compact
+    filenames = parsed_headers.flat_map do |headers|
+      next [] unless (header = headers["content-disposition"])
 
-    time =
-      lines.map { |line| line[/^Last-Modified:\s*(.+)/i, 1] }
-           .compact
+      [*parse_content_disposition.call("Content-Disposition: #{header}")]
+    end
+
+    time = parsed_headers
+           .flat_map { |headers| [*headers["last-modified"]] }
            .map { |t| t.match?(/^\d+$/) ? Time.at(t.to_i) : Time.parse(t) }
            .last
 
-    file_size =
-      lines.map { |line| line[/^Content-Length:\s*(\d+)/i, 1] }
-           .compact
-           .map(&:to_i)
-           .last
+    file_size = parsed_headers
+                .flat_map { |headers| [*headers["content-length"]&.to_i] }
+                .last
 
     is_redirection = url != final_url
     basename = filenames.last || parse_basename(final_url, search_query: !is_redirection)
diff --git a/Library/Homebrew/test/download_strategies/curl_github_packages_spec.rb b/Library/Homebrew/test/download_strategies/curl_github_packages_spec.rb
index 60e19b9db4..1cda9b052b 100644
--- a/Library/Homebrew/test/download_strategies/curl_github_packages_spec.rb
+++ b/Library/Homebrew/test/download_strategies/curl_github_packages_spec.rb
@@ -9,12 +9,38 @@ describe CurlGitHubPackagesDownloadStrategy do
   let(:name) { "foo" }
   let(:url) { "https://#{GitHubPackages::URL_DOMAIN}/v2/homebrew/core/spec_test/manifests/1.2.3" }
   let(:version) { "1.2.3" }
-  let(:specs) { {} }
+  let(:specs) { { headers: ["Accept: application/vnd.oci.image.index.v1+json"] } }
   let(:authorization) { nil }
+  let(:head_response) do
+    <<~HTTP
+      HTTP/2 200\r
+      content-length: 12671\r
+      content-type: application/vnd.oci.image.index.v1+json\r
+      docker-content-digest: sha256:7d752ee92d9120e3884b452dce15328536a60d468023ea8e9f4b09839a5442e5\r
+      docker-distribution-api-version: registry/2.0\r
+      etag: "sha256:7d752ee92d9120e3884b452dce15328536a60d468023ea8e9f4b09839a5442e5"\r
+      date: Sun, 02 Apr 2023 22:45:08 GMT\r
+      x-github-request-id: 8814:FA5A:14DAFB5:158D7A2:642A0574\r
+    HTTP
+  end
 
   describe "#fetch" do
     before do
       stub_const("HOMEBREW_GITHUB_PACKAGES_AUTH", authorization) if authorization.present?
+
+      allow(strategy).to receive(:system_command)
+        .with(
+          /curl/,
+          hash_including(args: array_including("--head")),
+        )
+        .twice
+        .and_return(instance_double(
+                      SystemCommand::Result,
+                      success?:    true,
+                      exit_status: instance_double(Process::Status, exitstatus: 0),
+                      stdout:      head_response,
+                    ))
+
       strategy.temporary_path.dirname.mkpath
       FileUtils.touch strategy.temporary_path
     end
diff --git a/Library/Homebrew/test/download_strategies/curl_post_spec.rb b/Library/Homebrew/test/download_strategies/curl_post_spec.rb
index c9e7983f26..cdb73bf917 100644
--- a/Library/Homebrew/test/download_strategies/curl_post_spec.rb
+++ b/Library/Homebrew/test/download_strategies/curl_post_spec.rb
@@ -10,9 +10,28 @@ describe CurlPostDownloadStrategy do
   let(:url) { "https://example.com/foo.tar.gz" }
   let(:version) { "1.2.3" }
   let(:specs) { {} }
+  let(:head_response) do
+    <<~HTTP
+      HTTP/1.1 200\r
+      Content-Disposition: attachment; filename="foo.tar.gz"
+    HTTP
+  end
 
   describe "#fetch" do
     before do
+      allow(strategy).to receive(:system_command)
+        .with(
+          /curl/,
+          hash_including(args: array_including("--head")),
+        )
+        .twice
+        .and_return(instance_double(
+                      SystemCommand::Result,
+                      success?:    true,
+                      exit_status: instance_double(Process::Status, exitstatus: 0),
+                      stdout:      head_response,
+                    ))
+
       strategy.temporary_path.dirname.mkpath
       FileUtils.touch strategy.temporary_path
     end
diff --git a/Library/Homebrew/test/download_strategies/curl_spec.rb b/Library/Homebrew/test/download_strategies/curl_spec.rb
index bd66ae2978..1739ebe7f9 100644
--- a/Library/Homebrew/test/download_strategies/curl_spec.rb
+++ b/Library/Homebrew/test/download_strategies/curl_spec.rb
@@ -12,6 +12,10 @@ describe CurlDownloadStrategy do
   let(:specs) { { user: "download:123456" } }
   let(:artifact_domain) { nil }
 
+  before do
+    allow(strategy).to receive(:curl_head).and_return({ responses: [{ headers: {} }] })
+  end
+
   it "parses the opts and sets the corresponding args" do
     expect(strategy.send(:_curl_args)).to eq(["--user", "download:123456"])
   end
@@ -190,48 +194,48 @@ describe CurlDownloadStrategy do
   end
 
   describe "#cached_location" do
-    subject(:cached_location) { described_class.new(url, name, version, **specs).cached_location }
+    subject(:cached_location) { strategy.cached_location }
 
     context "when URL ends with file" do
-      it {
+      it "falls back to the file name in the URL" do
         expect(cached_location).to eq(
           HOMEBREW_CACHE/"downloads/3d1c0ae7da22be9d83fb1eb774df96b7c4da71d3cf07e1cb28555cf9a5e5af70--foo.tar.gz",
         )
-      }
+      end
     end
 
     context "when URL file is in middle" do
       let(:url) { "https://example.com/foo.tar.gz/from/this/mirror" }
 
-      it {
+      it "falls back to the file name in the URL" do
         expect(cached_location).to eq(
           HOMEBREW_CACHE/"downloads/1ab61269ba52c83994510b1e28dd04167a2f2e8393a35a9c50c1f7d33fd8f619--foo.tar.gz",
         )
-      }
+      end
     end
 
     context "with a file name trailing the URL path" do
       let(:url) { "https://example.com/cask.dmg" }
 
-      it {
+      it "falls back to the file extension in the URL" do
         expect(cached_location.extname).to eq(".dmg")
-      }
+      end
     end
 
     context "with a file name trailing the first query parameter" do
       let(:url) { "https://example.com/download?file=cask.zip&a=1" }
 
-      it {
+      it "falls back to the file extension in the URL" do
         expect(cached_location.extname).to eq(".zip")
-      }
+      end
     end
 
     context "with a file name trailing the second query parameter" do
       let(:url) { "https://example.com/dl?a=1&file=cask.zip&b=2" }
 
-      it {
+      it "falls back to the file extension in the URL" do
         expect(cached_location.extname).to eq(".zip")
-      }
+      end
     end
 
     context "with an unusually long query string" do
@@ -253,10 +257,10 @@ describe CurlDownloadStrategy do
         ].join
       end
 
-      it {
+      it "falls back to the file extension in the URL" do
         expect(cached_location.extname).to eq(".zip")
         expect(cached_location.to_path.length).to be_between(0, 255)
-      }
+      end
     end
   end
 end
diff --git a/Library/Homebrew/utils/curl.rb b/Library/Homebrew/utils/curl.rb
index 7c89caae16..2687ad268d 100644
--- a/Library/Homebrew/utils/curl.rb
+++ b/Library/Homebrew/utils/curl.rb
@@ -141,7 +141,7 @@ module Utils
       raise Timeout::Error, result.stderr.lines.last.chomp if timeout && result.status.exitstatus == 28
 
       # Error in the HTTP2 framing layer
-      if result.status.exitstatus == 16
+      if result.exit_status == 16
         return curl_with_workarounds(
           *args, "--http1.1",
           timeout: end_time&.remaining, **command_options, **options
@@ -149,7 +149,7 @@ module Utils
       end
 
       # This is a workaround for https://github.com/curl/curl/issues/1618.
-      if result.status.exitstatus == 56 # Unexpected EOF
+      if result.exit_status == 56 # Unexpected EOF
         out = curl_output("-V").stdout
 
         # If `curl` doesn't support HTTP2, the exception is unrelated to this bug.
@@ -207,6 +207,28 @@ module Utils
       curl_with_workarounds(*args, print_stderr: false, show_output: true, **options)
     end
 
+    def curl_head(*args, **options)
+      [[], ["--request", "GET"]].each do |request_args|
+        result = curl_output(
+          "--fail", "--location", "--silent", "--head", *request_args, *args,
+          **options
+        )
+
+        # 22 means a non-successful HTTP status code, not a `curl` error, so we still got some headers.
+        if result.success? || result.exit_status == 22
+          parsed_output = parse_curl_output(result.stdout)
+
+          # If we didn't get a `Content-Disposition` header yet, retry using `GET`.
+          next if request_args.empty? &&
+                  parsed_output.fetch(:responses).none? { |r| r.fetch(:headers).key?("content-disposition") }
+
+          return parsed_output if result.success?
+        end
+
+        result.assert_success!
+      end
+    end
+
     # Check if a URL is protected by CloudFlare (e.g. badlion.net and jaxx.io).
     # @param response [Hash] A response hash from `#parse_curl_response`.
     # @return [true, false] Whether a response contains headers indicating that