Set oven control to broil. Shape beef into patties, each about 3/4 inch thick. Place patties on rack in broiler pan. Broil with tops 3 to 4 inches from heat 5 to 7 minutes on each side for medium, turning once, until no longer pink in center and juice is clear. For adults, spread patties with pesto. For adults and children, top each patty with a slice of cheese. Broil just until melted. Serve patties in buns.