Preheat oven to 350°F. Mist a 9-by-13-inch baking dish with cooking spray.
In a large skillet, warm oil over medium heat. Add onion and bell pepper; sauté until onion is translucent, about 4 minutes. Add garlic and chili powder and sauté 1 minute.
Add chicken and chilies; season with salt and pepper. Raise heat to high. Sauté until chicken is cooked through, about 5 minutes. Pour in enchilada sauce. Bring to a boil. Spoon mixture into baking dish.
In a large bowl, combine cornbread and buttermilk. Sprinkle 1/2 cup cheese over chicken mixture; spread cornbread mixture evenly on top. Sprinkle with remaining cheese. Bake until top is golden, about 20 minutes.