Heat a drizzle of oil or pat of butter in a small skillet over medium-high heat. Lightly beat the eggs and pour them into the hot pan; sprinkle with salt and pepper and cook, lifting the edge of the egg with a fork or spatula to let the uncooked egg run underneath, until the eggs are set. (Alternatively, you could scramble them.)
When the eggs are set, fold in half, and then in half again to make a wedge shape. Place a piece of cheese on a slice of bread, top with the egg, bacon or ham, another slice of cheese and another slice of bread. Spread the outside with butter or mayonnaise and return to the skillet to cook until golden on both sides and heated through. Serve with hot sauce.