Special equipment: 4 cups wood chips or chunks (preferably hickory), soaked for 1 hour in water to cover, then drained
Generously season the mutton with about 1 tablespoon each of salt and pepper. Set aside.
Make the basting sauce:
Combine the vinegar, Worcestershire sauce, salt, lemon juice, and pepper with 1 1/2 cups water in a nonreactive saucepan and bring to a boil over high heat.
Make the dipping sauce:
Combine the Worcestershire sauce, vinegar, lemon juice, brown sugar, pepper, coarse and onion salts, garlic powder, MSG, if using, allspice, and 2 cups water in a large nonreactive saucepan, bring to a boil over high heat, and cook until richly flavored and slightly reduced, about 5 minutes. Transfer the sauce to a nonreactive serving bowl to cool.
Set up the grill for indirect grilling and preheat to medium-low. If using a charcoal grill, preheat it to medium, then toss 1 cup of the wood chips or chunks on the coals. If using a gas grill, place all of the wood chips or chunks in the smoker box or in a smoker pouch and run the grill on high until you see smoke, then reduce the heat to medium.
When ready to cook, place the mutton, fat side up, in the center of the hot grate, over the drip pan and away from the heat, and cover the grill. Cook the mutton until it is fall-off-the-bone tender, 4 to 6 hours.
To test for doneness, insert an instant-read meat thermometer into the thickest part of the mutton but not touching the bone: The internal temperature should be about 190 degrees F. Baste the mutton with the basting sauce every half hour. If the mutton starts to burn, cover it loosely with aluminum foil. If using a charcoal grill, every hour you'll need to add 12 fresh coals and 1/2 cup of the wood chips or chunks to each side.
Transfer the grilled mutton to a cutting board and let it rest for 5 minutes. Slice the mutton thinly across the grain or finely chop it with a cleaver. Spoon half of the dipping sauce over the meat. Serve the mutton on toasted or grilled hamburger buns or slices of white bread or all by itself, passing the remaining dipping sauce on the side.
Variation: You can substitute a 5- pound leg of lamb for the mutton. The cooking time will be closer to 4 hours. To test for doneness, insert an instant-read meat thermometer into the thickest part of the leg but not touching the bone: The internal temperature should be about 190 degrees F.
Excerpted with permission from BBQ USA: 425 Fiery Recipes from All Across America by Steven Raichlen (Workman Publishing, 2003)