Preheat your oven to 350°F (175°C).
In a medium mixing bowl, combine the sour cream, cream of chicken soup, diced green chilies, garlic powder, onion powder, cumin, salt, and black pepper. Whisk until well combined.
In a large skillet, heat the shredded chicken over medium heat until warmed through, about 5 minutes.
In the baking dish, spread a thin layer of the sour cream mixture on the bottom.
Layer 4 corn tortillas over the sauce, overlapping them slightly.
Spread half of the shredded chicken over the tortillas, then drizzle with one-third of the remaining sour cream mixture.
Sprinkle with half of the cheddar and Monterey Jack cheeses.
Repeat the layers with 4 more tortillas, the remaining chicken, another third of the sour cream mixture, and the remaining cheese.
Pour the remaining sour cream mixture over the top layer of cheese.
Cover the baking dish with aluminum foil and bake in the preheated oven for 20 minutes.
Remove the foil and bake for an additional 10 minutes until the cheese is bubbly and slightly golden.
Remove from the oven and let it cool for a few minutes before serving. Garnish with fresh cilantro if desired.