In a large skillet, melt butter over medium high heat. Crack eggs in pan and cook to desired firmness. Just before eggs are cooked, place a slice of cheese over each egg.
After cheese has melted, place each egg on a toasted slice of bread. Season eggs with salt and pepper. Spread mayonnaise and ketchup on remaining slices of bread and cover eggs with bread to make 4 sandwiches. Serve warm.