This is my granddaughter M.'s favorite breakfast while at Grandma's house. She just loves the yellow "egg gravy." If you don't care for the "gravy," just break the yolk when you add your egg to the skillet. NOTE: Especially good when sprinkled with black truffle sea salt!
Place bread on a clean, flat surface and, using a 3 inch diameter biscuit cutter or rim of a drinking glass, very firmly press into bread and twist to cut through bread. Remove and reserve the round of bread.
Melt butter in a small nonstick skillet over medium heat.
Remove from heat and add the bread "frame" and the round.
Turn the frame and round over to coat both sides with the melted butter, then return skillet to medium heat.
Crack egg and pour into hole in the bread frame.
Watch carefully and flip the round, to brown both sides, and turn over the egg in the frame when the white is almost completely opaque (about 1 1/2-2 minutes.)
Reduce heat to low and cook for about 15-30 seconds (according to the yolk firmness you prefer.)
Remove to warm plate and season as desired. Black truffle sea salt is highly recommended (the "real" stuff is available at myspicesage.com.)