I highly recommend you go ahead and bake your bacon. Preheat your oven to 350 degrees. Cut bacon in half and place on a baking rack that is nested in a baking sheet. Bake bacon for about 20 minutes or until brown and crispy.
You can cook this on the stove top as well. In a small bowl combine 2 eggs and 2 tablespoons of half and half. Whisk together well. Pour eggs over a hot griddle that two teaspoons of butter have been melted on. Cook eggs on medium-low heat until they are done.
Do not disturb the eggs while cooking. When eggs are almost done cut the eggs in half and fold eggs into smaller portions. Toast muffin, and butter both sides. Assemble sandwich by placing the eggs on the bottom bun, then the cheese slices, and finally add the 4 pieces of cooked bacon. Top with the remaining muffin top.