Preheat the broiler and position the rack 6-inches from the heat.
Spread a bit of butter on one side of the first slice of bread and a bit more on one side of the second slice of bread.
Heat an oven safe skillet over medium heat. Add once slice of bread, butter side down, into the pan.
Place the cheese slices on top then add the remaining slice of bread, butter side up.
Cook the sandwich until the bottom is lightly browned, about 1 to 1½ minutes.
Remove the skillet from the heat. Place the sandwich on a cutting board, cooked side down and stamp out a hole in the center using a small biscuit cutter.
Return the sandwich and cut-out to the skillet, browned side up and melt a touch more butter in the hole.
Crack the egg into the hole and sprinkle with sea salt and freshly cracked pepper, to taste. Cook over medium heat for about 1 minute, to set the bottom.
Place the oven safe skillet under the broiler and cook until the top is browned and the egg whites are just set, but the yolk is still runny, about 1½ minutes.
Remove from the oven and serve immediately with the cut-out on the side. Enjoy!