Mix ground beef, onion and seasonings in medium bowl until well blended. Shape into 4 patties. Brush bell peppers with oil.
Grill patties and bell peppers over medium heat 4 to 6 minutes per side or until burgers are cooked through (internal temperature of 160°F). Add cheese slices to burgers 1 minute before cooking is completed. Toast rolls on the grill, open-side down, about 30 seconds.
Cut bell peppers into thin strips. Serve burgers on toasted rolls topped with bell peppers. Garnish with desired condiments and toppings.