Place bacon in a large, deep skillet. Cook over medium high heat until evenly brown, but still flexible. Wrap bacon slice around the inside of a muffin cup. Place a teaspoon of butter (or bacon grease) in the bottom of muffin cup. Drop in egg.
Bake in preheated oven for 10 to 15 minutes. Place 1/4 slice of cheese over egg, and continue cooking until cheese is melted and egg is cooked.