Prepare outdoor grill with medium-hot coals, or heat gas grill to medium-hot, or see Broiler Method and Stovetop Method, below.
Mix beef, onion, sauce, salt and pepper. Make 6 burgers, 3/4 inch thick.
Grill uncovered, 5 minutes. Turn over; grill until 160°F on instant-read thermometer, about 3 minutes.
Top burgers with cheese; grill to melt slightly. Toast rolls. Spread bottoms with mustard; top with burger, lettuce, onion, tomato, roll.