To prepare a Quarter Pounder with Cheese on the grill, you'll need to preheat your grill to medium-high heat (around 375°F or 190°C). Once the grill is heated, cook the patty for about 4-5 minutes per side, flipping only once. Then, add the cheese and cook for an additional 1-2 minutes, or until the cheese is melted to your liking. The total cooking time will depend on the thickness of the patty and the desired doneness. It's recommended to use a meat thermometer to ensure that the internal temperature of the burger reaches at least 160°F (71°C) for food safety.