Preheat a grill to medium high. Divide the beef into four 6-ounce portions. Gather each into a ball, then gently flatten into a 4 1/2-inch-wide patty about 3/4 inch thick (be careful not to overwork the meat). Press your thumb into the center of each patty to make a 1/2-inch-deep indentation (this prevents the patties from bulging as they cook). Season the patties with salt and pepper.
Lightly oil the grill grates. Grill the patties indentation-side up until they are marked and release easily from the grill, about 4 minutes. Flip and cook until slightly firm, 3 more minutes for medium doneness. For cheeseburgers, top each patty with 2 slices cheese during the last minute of cooking and cover to melt.
Transfer the burgers to a plate and let rest 5 minutes so the juices redistribute. Toast the buns on the grill, 30 seconds. Serve the burgers on the buns.