Preheat a large cast-iron skillet to medium hot. Take a few paper towels and fold them several times to make a thick square. Blot a small amount of oil on the paper towel and carefully and quickly wipe the hot skillet to make a nonstick surface.
Season the ground meat in a bowl with salt and pepper. Give it about 3 turns in the bowl with your hands or a big spoon and it's done. Shape into 4 patties. When the skillet is hot, put the burgers on the skillet and cook 4 minutes on the first side and 5 for the second side for rare; 7 minutes per side for medium, adding the cheese during the final minute or 2 to melt
. Remove the burgers to a plate. Rub the skillet with the folded paper towel again to clean it. Then toast the buns cut side down for about 1 minute, just to mark them. Serve the hamburgers in the buns with the accompaniments below.