Preheat your grill to medium heat and ensure the grates are clean and lightly oiled to prevent sticking.
Take each slice of cheese and fold it into quarters to form four small stacks.
Divide the ground turkey into eight equal portions, then flatten each portion into patties approximately 1/4 inch thick.
Position a cheese stack in the center of four of the patties, and then cover them with the remaining patties. Pinch the edges firmly to create a seal, ensuring the cheese remains enclosed. Adjust the edges to maintain an even thickness. Season both sides generously with salt and black pepper.
Place the patties on the prepared grill and cover. Cook for about six minutes on each side, or until the internal temperature reaches the desired doneness and the cheese has melted thoroughly.
Once cooked, transfer the patties to the buns and add your desired toppings. Allow the burgers to cool slightly before indulging to avoid burning your mouth on the hot cheese.
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