The traditional way, I was taught, is to use unseasoned meat, cheek is good, chuck works too, any meat that has connective tissue and responds to a long slow cook. Then wrap the unseasoned meat in a banana or maguey leaf and steam in a coal fired pit until tender. There is a place out here, that is known for their Barbacoa that uses a large pot, layers the beef cuts and offal as well, with maguey leaves, covers and roasts it for several hours. They add water from time to time, to keep the steam rolling. The flavor is added once the meat is pulled. The offal if offered separately and is also flavored after chopping.
me: I don't drink anymore
Yelonutz: me either, but, then again, I don't drink any less