Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, diced onion, green chilies, garlic powder, ground cumin, chili powder, salt, and pepper. Mix well until all ingredients are combined.
In a separate bowl, mix the sour cream with half of the enchilada sauce. Stir until smooth.
In the prepared baking dish, spread a thin layer of the sour cream mixture on the bottom.
Layer 5 corn tortillas on top of the sour cream mixture, overlapping slightly.
Spread half of the chicken mixture over the tortillas, then drizzle with one-third of the remaining enchilada sauce and sprinkle with one-third of the cheddar and Monterey Jack cheeses.
Repeat the layering process: add another layer of 5 tortillas, the rest of the chicken mixture, another drizzle of enchilada sauce, and the remaining cheeses on top.
Finally, pour the last of the sour cream mixture over the top layer.
Cover the baking dish with aluminum foil and bake for 20 minutes. Remove the foil and bake for an additional 10 minutes, or until the cheese is bubbly and golden.
Allow the casserole to cool for a few minutes before serving. Garnish with fresh cilantro if desired.