Preheat your oven to 350°F and spray a 9x13-inch baking dish with non-stick cooking spray. This will ensure the casserole comes out easily and cleanly once baked.
In a medium bowl, toss together the shredded chicken, 1 cup of shredded cheese, garlic powder, salt, and pepper. This savory mixture will form the heart of your casserole.
Melt the butter in a medium saucepan over medium heat. Add the flour, whisking constantly, to form a thick paste (roux). Gradually add the chicken broth, whisking as you go to create a smooth base. Stir in sour cream, cream cheese, and green chiles. Cook for 2–3 minutes until the sauce thickens to a creamy consistency. Remove from heat.
Cut tortillas into halves or quarters. Arrange a layer of tortillas to cover the bottom of your prepared baking dish. Spread one-third of the chicken mixture evenly over the tortillas, then pour one-third of the sauce on top. Repeat this process for two more layers, finishing with the remaining sauce.
Sprinkle the final cup of shredded cheese over the top layer, ensuring even coverage. Place the dish in your preheated oven and bake for 30 minutes, until the casserole is bubbling at the edges. For a golden cheese topping, broil on low for 2–3 minutes but keep a close eye to prevent burning.
Remove from the oven and allow the casserole to cool for 5–10 minutes. Garnish with fresh parsley or cilantro before serving for a pop of color and flavor.