1. Divide beef into 4 equal portions, and gently form each into a ball. Insert a piece of cheese in the center of each ball, and flatten into 1-inch-thick patties, pinching beef to enclose cheese.
2. Transfer to a plate; with thumb, make a shallow indentation in center of patties, taking care not to expose cheese.
3. Heat grill to high; lightly oil grates. Just before grilling, season patties with salt and pepper. Place on grill; cover, and cook to desired doneness, 2 to 4 minutes per side for medium-rare. Let burgers rest 3 to 4 minutes; serve on buns with desired toppings.

Serves 4.