Whisk the melted butter and flour in a small bowl; set aside. In a medium saucepan, add ground beef over medium heat, breaking apart with a spatula or large spoon. Cook, continuing to break apart, until cooked through. Carefully drain grease and return to stove. Add bacon, milk, yolks and pepper, stirring well. Bring to scalding, stirring frequently and add cheese, bacon and butter mixture(roux). Stir well and continue cooking and stirring until thick, creamy and cheese has completely melted. Serve hot.
If you decide to make this either a Deluxe or Royal version, simple add diced tomatoes at the very end or cook a quarter cup diced onion with burger.