Is there a way to get all commit history for a single branch?

I'm using this action like this (this works splendidly):

- name: Check Out Code
  uses: actions/checkout@v2
  with:
    ref: ${{ env.BRANCH }}
    fetch-depth: 0

I only need to get the entire commit history for just that one ${{ env.BRANCH }}. But using fetch-depth: 0 gets all commit history for all branches and tags, which is unnecessary in my case. Is there a way to get the entire commit history for just the branch referenced in the ref?

Start with the checkout action's handling of ref and fetch-depth, then review how Git fetches branch history versus all refs and tags. Done means the action can obtain the complete history for the requested branch without fetching unrelated branches or tags, with behavior covered by the relevant action tests or documentation.