Add 16 oz of liquid to drip tray and preheat Kenyon Grill to high.
Divide the meat into 4 equal portions. Gently form each portion into a 3/4-inch-thick burger. With your thumb, make a 1/4-inch-deep indentation in the center of each as this prevents the burgers from getting rounded tops during grilling. Season both sides of each burger with salt and pepper.
Place the patties on the grill; cover and cook to desired doneness, 2 to 4 minutes per side for medium-rare. Add the cheese to the top of the burgers during the last minute of cooking.
Serve burgers on buns with desired toppings.