PREPARE THE MEAT: Trim the fat from the meat; cut into 2 large pieces. Put meat into a large non-corrosive baking dish or pan.
PREPARE THE MARINADE/GLAZE: Heat a griddle or large cast-iron skillet over medium heat. Tear chiles into flat pieces and toast a few at a time, pressing them against the hot surface, until they crack and blister; flip them and press down again. Transfer chiles to a large bowl and cover with boiling water; weight down with a plate to keep them submerged, and soak at least 30 minutes. Meanwhile, roast the garlic in the same griddle or skillet, turning frequently, until soft inside and blackened outside, about 15 minutes. Cool and peel. Drain chiles, reserving 3/4 cup soaking liquid; put chiles into a blender with garlic, cloves, sesame seeds, vinegar, cumin, peppercorns or ground pepper, and salt. Process/blend until mixture is smooth; then strain through a medium-mesh sieve into a bowl. Remove 1/2 cup of mixture to a small bowl, and stir in the sugar; set aside to u se for the final glazing.
MARINATE THE MEAT: Spread the rest of the chile paste thoroughly over the meat. Cover completely and refrigerate at least 18 hours.
COOK (SLOW-STEAM) THE MEAT: Preheat the oven to 325 degrees. Use a deep wide roasting pan that has a tight lid. Put a roasting rack into the bottom of the pan (it must sit at least 1 inch above the bottom of the pan---if not, prop it up with custard cups, tin cans, etc.) Measure in 4 cups of water. Then lay the marinated meat onto the rack and spread any marinade remaining in the marinating pan or dish. Cut a double thickness of heavy-duty foil to cover the roasting pan; place the pan lid over, making sure the pan is covered as tightly as possible. Bake 4 hours.
FINISHING THE BROTH: Remove the pan lid and foil; carefully remove the tender meat to a platter. Take out the rack; spoon the fat off the broth with a ladle. Measure out the broth into a 1-quart container; add water to equal 1 quart liquid if necessary, and pour into a saucepan. Puree the tomato in a blender and add it to the broth along with the oregano and cinnamon. Cover; simmer over medium-low heat 45 minutes. Season with salt.
GLAZE THE MEAT: Heat oven to 375 degrees. Remove meat from the bones, keeping pieces of meat as large as possible; discard bones, gristle and excess fat. Set meat on a baking sheet; brush lightly with reserved chile paste glaze, and bake 10 minutes to set the glaze.
TO SERVE: Keep tortillas warm in a towel-covered basket. Serve the broth in a tureen. Present the meat on a large platter, or slice meat across the grain to serve it in deep plates, awash in the broth. Combine onion and coriander in a small bowl to pass with the lime at the table.