In a large bowl, mix all ingredients together for the burger patties. Divide into 4 even balls and form into patties with a slight depression in the middle for even cooking time. Grill burgers about 5 minutes per side or until done to your liking. Once you flip your patties once, top with a slice of cheese and cover to melt. Toast buns in the last two minutes of cooking, if desired. Remove everything from grill.
In a small bowl, stir together green chiles and enchilada sauce. Microwave to warm and set aside.
Build burger by topping cheeseburger with lots of green chile sauce and any other desired toppings.