To tell if a stuffed burger is done, the most reliable method is to use an instant-read meat thermometer. Insert the thermometer into the thickest part of the patty, avoiding the cheese filling for an accurate reading of the meat's temperature. For safety and optimal taste, the internal temperature should reach at least 160°F (71°C) for ground beef, which ensures that harmful bacteria are destroyed. Additionally, observe the burger's exterior; it should be well-browned and slightly firm to the touch. If you notice clear juices running when you lightly press the patty, it’s a good indication that the burger is cooked through. Avoid cutting into the burger to check doneness, as this releases the juices and can result in a drier patty.