To prepare the beef, put it in a large saucepan or small kettle. Add the broth, water, and the whole garlic. Bring to the boil and let simmer 2 hours, or until quite tender. Drain but reserve about ¼cup of the cooking liquid. Shred the meat. If the meat is not tender enough, chop it in a food processor.
To prepare the cornmeal mush, put the cornmeal in a heavy saucepan and add the salt, broth, and lard. Bring to the boil, stirring constantly with a wire whisk. Cook until thickened. Continue cooking, stirring, about 5 minutes. Set aside. The mush should be slightly cooled, but do not let it get cold or it will not be manageable.
Preheat the oven to 400 degrees.
To make the filling, heat the bacon fat in a saucepan and add the onion, minced garlic, and chopped sweet peppers. Cook, stirring, until the vegetables are wilted. Add the shredded meat, chili powder, cumin, oregano, coriander, salt and pepper to taste, tomatoes, corn, and hot chilies. Add the reserved ¼cup broth. Stir.
Butter a 10-cup baking dish.
Add enough of the cornmeal mush to coat the bottom and sides of the dish. Leave enough mush to cover the top. Spread the mush in the dish as neatly as possible over and around the bottom and sides. Add the filling. Smooth it over. Add the remaining mush and smooth it over. Dot the top with butter. Place the dish in the oven and bake about 45 minutes, until piping hot throughout and nicely browned on top.