Trim external fat on beef brisket to 1/4 inch. Combine paprika and 1/2 tsp of the black pepper; rub evenly over surface of beef brisket. Place brisket, fat side down, in 11 1/2 X 9" disposable foil pan. Add 1 cup water. Cover pan tightly with aluminum foil. Place in center of grid over very low coals (use a single layer of coals with space in between each); cover cooker. Cook 5 - 6 hours, turning brisket over every 1 1/2 hours; use baster to remove fat from pan as it accumulates.
Add 1/2 cup water, if needed, to pan during cooking. (Add just enough briquette during cooking to keep coals at a very low temperature). Remove brisket from pan; place on grid, fat side down, directly over very low coals. Reserve pan dripping. Cover; continue cooking for 30 minutes to 1 hour. Meanwhile, skim fat from pan drippings; reserve 1 cup drippings. Melt butter in medium saucepan over medium heat. Add onion; cook until tender crisp. Add reserved pan drippings, remaining 1/2 teaspoon black pepper, the catsup, lemon juice, worcestershire sauce and hot pepper sauce; simmer 15 minutes.
Carve brisket into thin slices across the grain; serve with sauce. Garnish with fresh peppers and lemon and lime slices. Note: For a smokier flavor, soak oak, pecan, mesquite or hickory chips in water 30 minutes and add to very low coals. Source: National Live Stock and Meat Board.
1 Boneless beef brisket (6 to- 8 pounds)
2 ts Paprika
1 ts Ground black pepper, divided
1 tb Butter
1 ea Medium onion, grated
1 1/2 c Catsup
1 tb Fresh lemon juice
1 tb Worcestershire sauce
1 ts Hot pepper sauce