Preheat the oven to 350˚F.
Mix the cheeses and then sprinkle 1 cup of the cheese (about 2/3) in the bottom of a casserole dish. Then dollop the green chiles evenly over the cheese.
Place the flour in the bottom of a bowl and use a whisk to slowly mix in a little of the milk to make a paste, then continue to pour the milk in while whisking until it is all smoothly combined. Then add the eggs into the milk, season with salt and pepper, and use the whisk to combine well. Pour the mixture into the casserole dish over the cheese and chiles.
Top the casserole with remaining cheese and then bake on the middle rack of the oven for 25-35 minutes or until eggs are set in the middle.
Remove from oven and let sit for 5 minutes then serve hot. Enjoy!