Preheat the oven to 350°F (175°C).
In a medium saucepan, melt 2 tablespoons of unsalted butter over medium heat.
Whisk in 2 tablespoons of all-purpose flour and cook for 1-2 minutes until lightly golden, stirring constantly.
Gradually whisk in 1 cup of milk and continue to cook, stirring frequently, until the sauce thickens, about 3-5 minutes.
Remove the saucepan from heat and stir in 1 1/2 cups shredded nacho cheese blend until melted and smooth. Set aside.
In a large mixing bowl, combine shredded cooked chicken, 2 cups shredded cheddar cheese, 1 cup shredded Monterey Jack cheese, condensed cream of chicken soup, 1 cup sour cream, 1/2 cup milk, diced green chilies, garlic powder, onion powder, black pepper, and salt. Mix well.
Gently fold in half of the Nacho Cheese Doritos into the chicken mixture.
Spread half of the chicken mixture evenly in a 9×13 inch casserole dish.
Drizzle half of the prepared nacho cheese sauce over the chicken mixture layer.
Sprinkle half of the remaining Doritos over the cheese sauce.
Repeat layering with the remaining chicken mixture, remaining cheese sauce, and remaining Doritos.
Top the casserole with any remaining shredded cheddar and Monterey Jack cheese if desired.
Bake uncovered in the preheated oven for 25-30 minutes, until the casserole is bubbly and the top is golden brown.
Remove from oven and let rest for 5 minutes before serving.