Place the ground beef in a bowl and season with salt and pepper. Divide the mixture into 8 equal patties. Make a depression in the center of each patty and place 1 tablespoon cheese in the center of the meat. Form meat around the cheese to enclose it. Then, gently press down on the center creating a slight depression in each burger; repeat with remaining portions of meat. This will prevent the burger from having a bulge and the burger will be thick but flat and evenly cooked. Place in the refrigerator while you prepare the fire.
Prepare a charcoal fire using about 6 pounds of charcoal and burn until the coals are completely covered with a thin coating of light gray ash, 20–30 minutes. Spread the coals evenly over the grill bottom, position the grill rack above the coals and heat until medium-hot (when you can hold your hand 5 inches above the grill surface for no longer than 3 or 4 seconds). Or, for a gas grill, turn on all burners to high; close the lid and heat until very hot, 10–15 minutes.
Remove the patties from the refrigerator to take the chill off. Scrape the hot grill rack clean with a wire brush. Lightly dip wadded paper towels in the oil; holding the wad with tongs, wipe the grill rack.
Grill patties, uncovered, without pressing down on them, until well-seared on the first side, about 3 minutes. Flip burgers with a barbecue spatula; continue grilling until medium-rare, an additional 3–4 minutes. Transfer burgers to a warm platter.