The meat: Trim most of the fat from the meat (it is strong tasting); if it is a goat hindquarter, cut into 2 pieces with a cleaver, severing it through the joint at the top of the leg. Place in a large noncorrosive dish.
The chile marinade: Heat a griddle or heavy skillet over medium heat. Tear the chiles into flat pieces and toast them a few at a time, pressing them against the hot surface with a metal spatula until they crackle and blister, then flipping them over and pressing them again. Cover with boiling water, weight with a plate to keep them submerged and soak 30 minutes. Roast the garlic on the hot griddle or skillet, turning frequently, until soft inside and blackened outside, about 15 minutes. Cool and peel.
Drain the chiles and place in a blender jar with garlic, 1/4 teaspoon clove, 2 teaspoons lightly toasted sesame seeds and vinegar. Pulverize the cumin and peppercorns in a mortar or spice grinder, and add to the blender along with the salt and 3/4 cup water. Blend until smooth, then strain through a medium-mesh sieve. Remove 1/2 cup, stir in the sugar, cover and set aside for the final glazing. Spread the rest of the chile paste over the meat, cover and refrigerate overnight (at least 18 hours).
Slow-steaming: Preheat the oven to 325 degrees F. Set a roasting rack into a deep, wide kettle, a roasting pan with a rack or a stockpot. If it doesn=t sit at least 1-inch above the bottom of the pot, prop it up on custard cups, tin cans or the like. Measure in 4 cups of water, then lay the marinated meat on the rack and spread any remaining marinade over it.
Add water to the masa (or masa harina mixture) to make a soft dough. Roll tennis ball-size pieces between your palms to make 3/4-inch ropes, then press them gently all around the top edge of your pot. Set the lid in place and press it into the masa to seal. Bake for 4 hours.
Finishing the broth: Break the seal by tapping the hardened masa with the back of a cleaver or mallet, and take off the lid; then carefully remove the tender meat. Take out the rack, spoon the fat off the broth, then measure it. You need at least 1 quart, if necessary, add water to bring it to that level. Pour the broth into a small saucepan. Puree the tomato in a blender or food processor, add it to the broth along with the oregano, cover and simmer over medium-low heat for 45 minutes. Season with salt.
Glazing and serving the birria: Shortly before serving, remove the bones, large pieces of gristle and excess fat from the meat, keeping the pieces of meat as large as possible. Set the meat on a baking sheet, brush lightly with the reserved chile paste glaze, then bake for 10 minutes to set the glaze.
Either present the meat on a large platter and pass the warm broth separately, or slice the meat across the grain and serve it in deep plates, awash in the broth. Mix the onion and fresh coriander, and pass it with the lime at the table.
Suggested Drink: Triple Distilled Perfidia Plata Tequila Sol Beer Sangrita