Combine Ground Beef, chopped onion and 2 tablespoons barbecue sauce in medium bowl, mixing lightly but thoroughly. Shape into four 1/2-inch thick patties.
Place patties on grid over medium, ash-covered coals. Grill, covered, 8 to 10 minutes (over medium heat on preheated gas grill, 7 to 9 minutes) until instant-read thermometer inserted horizontally into center registers 160°F, turning occasionally. About 1 minute before burgers are done, brush with remaining 2 tablespoons barbecue sauce and top with cheese.
Line bottom half of each bun with lettuce, sliced red onion and tomato, as desired; top with burger. Close sandwiches.
Nutrition information per serving: 430 Calories; 150.3 kcal Calories from fat; 16.7 g Total Fat; 7.7 g Saturated Fat; 0.1 g Trans Fat; 1.1 g Polyunsaturated Fat; 3.6 g Monounsaturated Fat; 105 mg Cholesterol; 578 mg Sodium; 30 g Total Carbohydrate; 3.6 g Dietary Fiber; 8.7 g Total Sugars; 31 g Protein; 0 g Added Sugars; 269.1 mg Calcium; 4.3 mg Iron; 425 mg Potassium; 0 mcg Vitamin D; 0.3 mg Riboflavin; 8.6 mg NE Niacin; 0.4 mg Vitamin B6; 2.8 mcg Vitamin B12; 226 mg Phosphorus; 6.5 mg Zinc; 39.9 mcg Selenium; 95.8 mg Choline;