Preheat oven to 350°F and grease a 9x13-inch baking dish.
In a large skillet, melt butter over medium heat. Sauté onion and bell pepper until softened, about 5 minutes. Add garlic and cook 1 minute more.
In a large bowl, combine both cream soups, Rotel tomatoes, sour cream, chili powder, and cumin. Stir in the sautéed vegetables.
Layer half of the tortilla strips in the bottom of the prepared baking dish.
Top with half the chicken, half the soup mixture, and 1½ cups of cheddar cheese.
Repeat layers with remaining tortillas, chicken, soup mixture, and top with remaining cheddar and all of the Monterey Jack cheese.
Bake uncovered for 40-45 minutes until bubbly and cheese is golden. Let rest 10 minutes before serving.