Combine onions, bell peppers, oil and 2 teaspoons seasoning in a mixing bowl. Stir to evenly coat. Grill vegetables 8 to 10 minutes until vegetables are very tender and browned. Remove from grill and cover until burgers are done.
Season burgers on both sides with seasoning. Grill, turning once, until desired doneness or until the internal temperature reaches 160°F about 12 to 15 minutes. Top each burger with 1 slice of cheese just before removing from the grill.
Place buns on grill and toast for 1 to 2 minutes. Place burgers on toasted buns, top with onion and pepper mixture and second slice of cheese. Serve with pepperoncini, if desired.