Spread butter evenly on both sides of bread slices. Cut a circle from center of each slice, using a 2 to 3-inch round cutter. Centers can be cut from bread slices using a glass with a 2 to 3-inch diameter or a biscuit cutter.
Place 2 bread slices in large nonstick skillet with ovenproof handle(To make handle ovenproof, wrap it completely in aluminum foil), then heat to medium. Break egg shell gently and slip an egg into center of each slice. Cook until bottoms of eggs are set, 2 to 3 minutes; gently turn over. Cook until egg whites are completely set and yolks begin to thicken but are not hard.
Bread centers can be pan-toasted separately and eaten along with eggs-in-a-hole.
Sprinkle 1 tablespoons cheese onto each bread slice.
Broil 4 inches from heat just until cheese is melted, about 1 minute. Repeat to cook remaining eggs. Serve with salsa.