Preheat oven to 375°F and spray a 9x13-inch baking dish with cooking spray.
In a large bowl, combine shredded chicken, black beans, corn, green chiles, cumin, and 1 cup of the enchilada sauce.
Spread a thin layer of enchilada sauce on the bottom of the prepared dish, then layer with half the tortilla strips, half the chicken mixture, and 1 cup of cheese.
Repeat layers with remaining tortilla strips, chicken mixture, remaining enchilada sauce, and top with remaining 2 cups of cheese.
Cover with foil and bake for 20 minutes, then remove foil and bake an additional 10 minutes until cheese is melted and bubbly.
Let stand 5 minutes before serving with sour cream and fresh cilantro.