Lightly shape Ground Beef into four 3/4-inch thick patties. Coat onion with cooking spray. Place patties on grid over medium, ash-covered coals; arrange onion around patties. Grill, covered, 8 to 10 minutes (over medium heat on preheated gas grill, covered, 7 to 9 minutes) until instant-read thermometer inserted horizontally into center registers 160°F, turning occasionally. Season with OFBS Seasoning after turning, as desired. About 1 minute before the patties are done, top each with cheese.
(Cooking times are for fresh or thoroughly thawed ground beef. Ground beef should be cooked to an internal temperature of 160°F. Color is not a reliable indicator of ground beef doneness.)
Combine mayonnaise and mustard; spread on top and bottom halves of rolls. Serve burgers and onion in rolls with lettuce and tomato, as desired.