Combine ground beef with ½ of your diced Hatch Chile Peppers.
Divide ground beef into 4 equal sized patties, season with salt and pepper and grill until they reach your desired level of doneness.
To make the Hatch Chile Pepper cheese sauce melt 2 tablespoons butter in a saucepan over medium heat. Add 2 tablespoons flour and whisk until golden in color. Add 1 cup milk and reduce heat to low. Slowly add in 2 cups shredded Cheddar cheese and continue stirring until the sauce is smooth. Add remaining diced Hatch Chile Peppers and stir until combined. If you’d like a thicker sauce add more flour (1 tablespoon at a time) and if you’d like a thinner sauce add more milk (1 tablespoon at a time).
Assemble your burgers by topping each bottom bun with a burger, your choice of toppings, the Hatch Chile Pepper cheese sauce and finally a top bun.