Well, here's what I did last Sunday:
Bought 4 pounds of fresh Hatch green chiles, then roasted and peeled them. Took out the bulk of the seed pod, but didn't worry about leaving a number of seeds because I kinda like them in there. (Didn't de-vein, either.)
Took 2 pounds of locally-raised Texas grass-fed beef stew meat, cut into small bite-sized pieces, lightly floured, and browned that with a chopped Texas 1015 onion in bacon grease. I added beef stock (sorry, Kitchen Basics, not homemade) and put that into the oven at 325 for about 3 hours.
That morning, I had put about 4 ounces of dried hominy (please order from these guys:
http://www.welrp.org/nativeharvest/organicfoods.html ) to reconsitute in chicken stock (again, Kitchen Basics

).
When I took the beef out of the oven, I added the chile (cut up in the bowl), the hominy (with the remaining stock) some sea salt, fresh-ground black pepper, and about a teaspoon of ground comino. I debated about this, but I also ended up adding a large russet potato, cut into pieces about a half-inch.
I simmered it all another half hour, then dug in.
It was actually better reheated the next day.


Obviously, I had plenty left over (it was too hot for my wife, and my daughter wouldn't even consider eating it), so I have a couple of portions frozen for near-future enjoyment.