Mix mayonnaise and ketchup in a small bowl until smooth, then set aside.
Divide the ground beef into 4 equal portions, shape into patties slightly larger than the buns, season both sides with garlic powder and black pepper, and press a shallow indent in the center of each patty with your thumb.
Heat a cast iron skillet or grill over medium-high heat, cook the patties for 4 minutes on the first side without moving, flip once, and cook for 3 to 4 minutes until the internal temperature reaches 160°F / 71°C.
Place one cheese slice on each patty during the last 60 seconds of cooking and cover the pan to melt the cheese.
Toast the burger buns cut-side down in the same pan for 1 to 2 minutes until golden.
Spread the sauce on the bottom bun, layer with lettuce, tomato, the cheeseburger patty, and the top bun.