Git archive is what you're thinking of. I use it in my build system to output the repo state so users can download on my website! And it supports multiple formats, I use tar+gzip. I currently use --mirror and it seems to be working well and allow for easy automatic updates to mirror other remotes if need be. 

I've been trying to find ways to safely expose git without exposing my internal git server, so this nails it! And my software is serving itself :)