I am looking to gzip multiple files (into multiple .gz files) in a directory while keeping the originals.
I can do individual files using these commands:
Since you have multiple files, GNU Parallel might be useful:
find . -type f -name "*cache.html" | parallel gzip '<{} >{}.gz'
Watch the intro video for a quick introduction: https://www.youtube.com/playlist?list=PL284C9FF2488BC6D1