Re-Mash, Re-Brew?

We've been doing all grain for a few batches, usually 10 gallons at a time. However, we decided on a 5 gallon batch and mashed it up, boiled it, cooled it, and put in the carboy - all serene.

Then, perhaps because we were drinking quite a bit of a previous batch (which tasted marvelous), we threw in a pound of leftover grain in the mash tun, added hot water, and did a second round. We boiled with extra hops but in a reasonable, albeit random, way.

My question: has anybody had success with something like this? If so, what's a good 1-2 punch recipe? I feel like I read about this somewhere - about making a session brew after your original. Maybe not.

I believe the term is partiguyle. Why not toss the entire spent grain bill in instead of just a pound?

Sounds like partigyle to me. The second beer is referred to as a small beer in German brewing tradition and is the origin on triples, doubles and singles in Belgium. In my minimal experience with, I typically get half the gravity at half the volume of the original beer or one quarter gravity at the full batch size.