Line a baking sheet with waxed paper.
Gently combine the burger ingredients in a large bowl with your hands, taking care not to overwork the meat. Wet your hands in cold water before you form the mixture into chunks the size of tennis balls. Flatten them into patties, placing them on the baking sheet. Each patty will be about 1/2 lb before cooking. Place them in the freezer for 1 hour to firm them up.
Preheat your grill for medium direct heat. Take the burgers out of the freezer and grill them for 6 minutes per side, or until they are springy to the touch, glazing them on both sides with barbecue sauce. Top each patty with a slice of cheese for the last couple of minutes of cooking. Serve the burgers on buns with your favorite condiments.