Stir together ketchup, mayonnaise, pickles, salt, and pepper in a small bowl. Set aside.
Sprinkle salt over ground beef; divide into 8 equal portions, rolling each into a ball. Heat a 12-in. cast-iron skillet over medium-high. Add oil to hot skillet, and place 4 balls of beef in skillet. Using a spatula, press beef down into thin patties. Cook patties until browned and crisp, about 2 minutes; flip and crisp the other side. Top each patty with a cheese slice during last 30 seconds of cooking. Transfer to a plate, and repeat with remaining beef and cheese.