Trim most of fat from meat. If using goat hindquarter, cut in 2 pieces with cleaver, severing joint at top of leg
Heat heavy skillet over medium heat. Tear chiles into flat pieces and toast, few at a time, pressing them against hot surface with metal spatula, until they crackle and blister, about 5 minutes a side. Place in bowl and cover with boiling water, weighted with plate to keep submerged. Soak 30 minutes.
Roast garlic in same skillet until peel blackens and cloves are soft inside, 2-3 minutes. Cool and peel.
Drain chiles and puree in blender or food processor with garlic and vinegar. Add cumin, pepper, salt and 3/4 cup water and puree until smooth. Pres through sieve. Remove 1/2 cup and stirr in surar; set aside for glazing. Spread rest of chile paste over meat, cover and refrigerate 4 hours or overnight.
Set roasting rack in deep, wide pot atl least 1 inch above bottom of pot. Add 3 cups water. Lay marinated meat on rack, spreading any extra marinade on top. Cover pot with tight sealing lid. Bake at 325 degrees 3 hours.
Carefully remove meat from rack. Remove rack from pot and spoon fat from surface of broth. Measure out broth, adding water if necessary to make 1 quart, into saucepan. Puree tomato with oregano, add to broth and simmer over medium-low heat 20 minutes. Season with salt to taste.
Shortly before serving, remove bones, large pieces of gristle and excess fat from meat, keeping pieces of meat as large as possible. Set meat on baking sheet, brush lightly with reserved chile paste and bake a 350 degrees 10 minutes.
To serve, present meat on large platter and pass warm broth seprately, or slice meat across grain and serve it in broth soup plates. Pass onion, cilantro and limes.