How to Make It
Light 1 side of grill, heating to 350° to 400° (medium-high) heat; leave other side unlit. Toss together peppers and olive oil. Arrange peppers in a grill basket or on an aluminum-foil tray over unlit side, and grill, covered with grill lid, 10 to 15 minutes or until peppers begin to shrivel. Transfer peppers to lit side of grill, and grill, covered with grill lid, 8 to 10 minutes or until lightly charred, turning halfway through. Remove from grill to a wire rack, and cool completely (about 15 minutes).
Remove and discard stems; slice peppers in half lengthwise. Remove seeds, and sprinkle peppers with desired amount of salt.
Preheat both sides of grill to 350° to 400° (medium-high) heat. Shape ground chuck into 12 patties; sprinkle with desired amount of salt and pepper. Grill patties, without grill lid, 4 to 5 minutes on each side or to desired degree of doneness. Place 2 to 3 pepper halves on each patty; top with cheese. Grill, covered with grill lid, 1 to 2 minutes or until cheese melts.
Butter buns, and toast on grill. Serve patties on toasted buns with desired toppings.