Biggest Birria coupon. Birria is usually made with goat's meat or even with lamb or a combination of several types of meat. Beef Birria is more like a homemade version since beef is more accessible everywhere. Birria is a Mexican stew made with blended chile peppers simmered with beef stew meat. Birria, a classic Mexican dish that can be served as a stew or taco filling, can be made from whatever type of meat you like with this...