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1
Wash and griddle-dry the chiles by the directions below. Place in a deep bowl and cover generously with boiling water. Let soak for at least 20 minutes.
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2
Grind the cumin, cloves, allspice, oregano, and dried thyme (if using) together in an electric coffee or spice grinder or with a mortar and pestle.
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3
Drain the soaked chiles. Working in batches as necessary, place them in a blender with the ground herbs and spices (add fresh thyme at this point if using), garlic, onion, vinegar, salt, and about 1/2 cup water (or enough to facilitate the action of the blades). Process to a smooth puree (about 3 minutes on high), stopping occasionally to scrape down the sides with a rubber spatula. With a wooden spoon or pusher, for the puree through a medium-mesh sieve into a bowl. It should have the consistency of a thick but still moist paste.
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4
Season the pieces of goat or lamb with salt and pepper. Slather the seasoning paste all over the meat. Arrange in a large bowl (or any non-reactive container that's large enough), cover tightly with plastic wrap, and refrigerate overnight or for at least 4 hours. Remove from the refrigerator about 2 hours before beginning the cooking, to let the meat come to room temperature.
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5
Preheat the oven to 325u00b0F.
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6
Choose a deep roasting pan or baking dish large enough to hold the meat snugly. Scatter half of the avocado leaves across the bottom of the pan and arrange the meat on them. Scatter the remaining leaves over the meat. Cover the pan (wrapping very tightly with several layers of foil if there is no lid) and bake 6 to 7 hours (4 to 4 1/2 hours for the lamb). The meat should be almost falling off the bone.
