Cut the tops off the sweet peppers. Remove any ribs and seeds. For a charcoal grill, grill peppers on the rack of an uncovered grill directly over medium coals for 5 to 7 minutes or until pepper skins are lightly blistered and peppers are just tender, turning occasionally. (For a gas grill, preheat grill. Reduce heat to medium. Place peppers on grill rack over heat. Cover and grill as above.) Remove peppers from the grill; cool slightly. Stuff peppers with the cheese cubes.

In a medium bowl, combine ground beef and mesquite seasoning. Divide mixture into four portions. Shape each portion of the beef mixture around one of the stuffed peppers to completely enclose the pepper. Flatten slightly to form 3/4-inch-thick patties.

For a charcoal grill, grill patties on the rack of an uncovered grill directly over medium coals for 14 to 18 minutes or until an instant-read thermometer inserted into side of each patty registers 160 degrees F (insert the thermometer into the meat to the side of the pepper). (For a gas grill, place patties on grill rack over heat. Cover and grill as above.)

Place grilled patties on roll bottoms. If desired, spoon salsa on top of patties; top with roll tops.