Preheat the oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.
In a large bowl, mix the shredded chicken, green chiles, black beans, onion, 1 cup Monterey Jack cheese, cumin, garlic powder, salt, and pepper until combined.
Warm the tortillas in the microwave for about 30 seconds so they are soft and easy to roll.
Spread ½ cup enchilada sauce in the bottom of the baking dish. Fill each tortilla with the chicken mixture, roll up, and place seam-side down in the dish.
Pour the remaining enchilada sauce over the enchiladas. Sprinkle with the remaining Monterey Jack cheese and all of the cheddar cheese.
Cover with foil and bake for 20 minutes. Remove foil and bake an additional 15 minutes until bubbly.
Let rest for 5 minutes, garnish with fresh cilantro, and serve warm.