After looking over several recipes online (there is quite a variety) I decided to go with a simple braise using the "holy trinity," or sofrito in Italian cooking. I had a bag of dried porcini mushrooms in the pantry and decided to add those as well.
Oxtails seasoned with S&P

Browning on all sides with some EVOO

Ingredients for the braise. There's also a can of diced tomatoes, a sprig of fresh rosemary and a couple of bay leaves.

Everything gets incorporated on the stove. Then it goes in the oven at 300 deg for a couple of hours.

Once the meat is ready to fall off the bone, you take it out of the oven, pull the meat apart and discard the bones, add the meat back in and simmer for another 30 minutes. Served over some rotini pasta with some crusty bread on the side.

It was really tasty but I had to spoon about 3/4 cup of fat off the top before serving. I think I'll try the same recipe with short ribs next time.