Cook bacon in skillet until almost crisp. Set aside.
Make cheese sauce. Make a roux by whisking melted butter and flour in a saucepan over medium heat until smooth. Stir in milk to combine. Add extra sharp cheddar and American cheese until mixture thickens. Add salt and pepper to taste.
Cook Burger to order (4-5 minutes per side for medium rare).
Build Your Burger: Bottom Bun, Cole Slaw, Burger, Bacon, BBQ Sauce, Cheese Sauce, Frizzled Onions, Top Bun.