The poor rarely killed their animals as the live animal was worth much more for its milk, and hair.
When an animal was killed no part was wasted.
A recipe from a clay Tablet:

Head, legs and tail should be singed before putting them in the pot to boil.
Bring water to a boil.
Add fat, onions, samidu, leeks, garlic some blood of the goat, some fresh cheese.
Beat the whole together.

Sound Yummy?

You can bake some Ancient Flat Bread:

FLat Bread

14 oz. flour
1 cup of water
1/2 teaspoon of salt.

Mix the water, flour, and salt together slowly.
Knead the dough and form it into flat round patties.
Cover the dough with a cloth and let it sit over night.
Next day bake it in the oven 350 degrees for 30 minutes.

For an authentic Mesopotamian experience, eat it with a raw Onion!