Preheat oven to 350°F. Spray a 13x9-inch baking dish with nonstick cooking spray. Set aside.
In a medium bowl, whisk together half of the enchilada sauce and all of the sour cream until smooth. Spread half of the sour cream mixture in the bottom of the prepared baking dish.
In a medium bowl, stir together chicken, 1 cup of the Monterey Jack cheese, remaining enchilada sauce, green chiles, cumin, and garlic salt. Layer 6 tortillas in the bottom of the dish, overlapping the tortillas. Spoon chicken mixture over the tortillas. Arrange remaining 6 tortillas over the chicken mixture.
Pour remaining sour cream mixture over tortillas; sprinkle with remaining 1 cup of Monterey Jack cheese and the cheddar cheese. Gently tap pan on counter twice to settle ingredients.
Bake until bubbly and cheese melts, 20 to 25 minutes. Garnish with radish, cilantro, green onion, and tomato if desired.