Heat grill to medium-high. Form beef into four ½-inch-thick patties and season with ½ teaspoon each salt and pepper.
Grill the patties (do not press or flatten), 3 to 4 minutes per side for medium-rare. During the last minute of cooking, top with the cheese and cook, covered, until it melts.
Place the burgers on the buns and top with the barbecue sauce.