Combine ground beef and Worcestershire sauce in medium bowl, mixing lightly but thoroughly. Shape into twelve 1/2-inch thick mini patties.
Combine sauce ingredients in small saucepan; bring to a boil, stirring frequently. Remove from heat.
Preheat grill with medium heat, ash-covered coalsor place pineapple slices on rack in broiler pan so surface of pineapple is 3 to 4 inches from heat. Broil 3 to 4 minutes, turning once and brushing with sauce. Remove pineapple; keep warm. Place patties on rack in broiler pan so surface of beef is 3 to 4 inches from heat. Broil 7 to 8 minutes to medium (160°F) doneness, until not pink in center and juices show no pink color, turning halfway through and brushing with sauce. Season with salt, as desired.
Cut each pineapple slice into thirds. Line bottom of each roll with lettuce; top with a burger, then with a pineapple piece. Close sandwiches.
Makes 4 servings.
Nutrition information per serving: 583 calories; 30 g protein; 64 g carbohydrate; 22 g fat; 480 mg sodium; 107 mg cholesterol; 4.6 mg niacin; 0.4 mg vitamin B6; 2.3 mcg vitamin B12; 5.4 mg iron; 5.4 mg zinc.
Courtesy of the Cattlemen's Beef Board and the National Cattlemen's Beef Association.