Mix together egg, ground beef, salt, and minced onion. Grease 8-inch skillet (oven-proof); lightly pat half of the meat over bottom. Arrange cheese slices over meat layer and top with remaining meat, patting to make a smooth surface. Sprinkle with pepper and cut into 4 quarters. Cook over medium-high heat until bottom is nicely browned. Put skillet in oven and broil until top is browned and burger is cooked through.