Featured Gallery for posts

I’m trying to figure out the best way to store a “featured” gallery with each post. What I’m going for is something similar to:

http://www.fastcodesign.com/1672243/watch-a-jewelry-ad-worthy-of-magritte-and-max-headroom#2

This gallery will remain separate from the post (either above the post or otherwise) in the same way a feature image could be.

Ideally the user could set the gallery in the same way they set the feature image. Anyone have any suggestions? I have no problem writing the required plugin, but am having trouble figuring out where to start.