In small bowl, combine sauce ingredients (mayonnaise and Dijon mustard); set as ide. Shape ground beef into four 3/4" thick patties. Lightly brush oil onto cut side s of onion. Place patties and onions on grid over medium, ash covered coals. Gr ill, uncovered, 13 to 15 minutes or until centers are no longer pink and onions are tender, turning once. Season burgers with salt and pepper, if desired, aft er turning. Approximately 1 minute before burgers are done, top each burger wit h 2 slices cheese. Meanwhile, spread equal parts of sauce mixture on top half of each roll. Line b ottom half of each roll with lettuce and tomato; top with cheeseburger and onio n. Close sandwiches.