Preheat your oven to 350 degrees Fahrenheit. Lightly grease a 9 by 13 inch baking dish to prevent sticking.
In a bowl, mix the shredded chicken with half of the enchilada sauce and the cumin. This helps the chicken stay juicy and flavorful as it bakes.
If you want to soften the tortillas so they roll up easily, toss them with a teaspoon of oil and warm them in a skillet for a minute or two on each side, or microwave them in a damp towel for about 30 seconds.
In another bowl, whisk together the cream of chicken soup and sour cream until smooth. Stir in a splash of enchilada sauce to loosen things up a bit.
Spread a thin layer of the sour cream mixture across the bottom of the prepared dish. Layer three tortillas to cover the base. Break a couple of tortillas as needed to fit the pan.
Spread half of the chicken mixture over the tortillas, then drizzle with a quarter of the sour cream mixture. Sprinkle with a layer of cheddar and Monterrey Jack cheese.
Repeat the layers: a new tortilla layer, the remaining chicken mixture, more sour cream mix, and another sprinkle of cheese.
Finish with a final layer of tortillas, the remaining sour cream mixture, and a generous top with the remaining cheese.
Cover the pan with foil and bake for 20 minutes. Remove the foil and bake an additional 10 minutes until the cheese is bubbly and golden.
If you like a crisper top, run it under the broiler for 1-2 minutes watching closely so it doesn’t burn.
Let the casserole rest for about 5 minutes before serving. This helps it set and makes scooping easier.