Core and Julianne each half of the apple (don’t peel). Place 2 Tbs. of butter in the skillet. Add apple when the butter has melted. Sauté approximately 5 minutes until apple is tender. Set apple aside.
Shell the eggs and whisk together with milk and pepper. Again heat skillet and add last two tablespoons of butter. When butter has melted add egg mixture to the pan. Cook until the top of mixture is mostly cooked (Watch your stove heat and be careful not to burn the underside of the eggs).
Sprinkle apples over the top of eggs and add both cheeses evenly over the top of the apple. With a large spatula fold one side of the omelet over the other half. Turn heat down to low and cover pan. Cook for approximately 30 seconds or until cheese is melted. This large omelet can serve two. Serve immediately.