Heat Pan: Place a medium non-stick skillet over medium heat. Add butter to the pan and melt until bubbly, making sure it coats the bottom. It's ready when it sizzles with a drop of water on it. (Make sure it doesn't burn.)
Cut Hole in Bread: Meanwhile, use a cookie cutter, biscuit cutter, or a glass to cut a circle out of the middle of the bread.
Butter Bread & Add Egg to Skillet: To the hot skillet, place the bread slice and the cut-out circle side-by-side, making sure the bottoms get covered in butter, and flip them over. (You're not toasting the bread here but just buttering it.) Crack the egg directly into the hole. Sprinkle with salt and pepper, to taste.
Cook First Side: Cook for 2-3 minutes, or until the egg whites start to set and the bread gets golden brown. Watch closely. Tip: If you don't like a runny yolk, simply poke it and let it run out during this step. It will cook through by the end.
Cook Second Side: Using a spatula, carefully flip over the "egg in a hole" and the cut-out circle piece and cook for an additional 1-2 minutes, or until bread is toasted on the second side.