Preheat oven to 375°F and spray a 9x13-inch baking dish with cooking spray.
In a large bowl, combine shredded chicken, black beans, green chiles, cumin, garlic powder, and 1 cup of cheese.
Spread 1/3 cup enchilada sauce on the bottom of the baking dish, then layer 4 tortillas to cover the bottom.
Spread half the chicken mixture over tortillas, drizzle with 1/3 cup enchilada sauce, then repeat layers with remaining tortillas and chicken mixture.
Pour remaining enchilada sauce over the top and sprinkle with remaining 1 cup cheese.
Cover with foil and bake for 25 minutes, then remove foil and bake 10 more minutes until cheese is bubbly and golden.
Let stand 5 minutes, then top with dollops of sour cream and fresh cilantro before serving.