Cut a 2-inch hole in each slice of bread. Reserve rounds. Butter both sides of each slice.
Heat a nonstick skillet over medium heat. Place 3 slices of buttered bread in the skillet. Crack 1 egg into each hole. Cook until bottom of eggs begin to set and turn opaque, 2 to 3 minutes. Flip; cook until eggs are set and bread is golden brown, about 1 minute more. Repeat with remaining bread and eggs.
Serve with bread rounds for dipping into egg yolks.