Step 1

Preheat the oven to 375°F. Grease a 9-by-13-inch baking dish with oil.

Step 2

In a large Dutch oven, heat 1 tablespoon of the oil over medium heat. Add the onion, red bell pepper, yellow bell pepper, jalapeño, chili powder, cumin, salt, and pepper and cook until the vegetables are tender and lightly golden, 5 to 7 minutes. Stir in the cream of chicken soup, cream of mushroom soup, diced tomatoes with green chilies, and chicken broth and bring to a simmer. Reserve 1/2 cup of the sauce. Remove from the heat and fold in the chicken.

Step 3

Spread the reserved 1/2 cup sauce on the bottom of the prepared baking dish. Place half of the torn tortillas on top of the sauce. Spoon in half of the chicken mixture. Sprinkle on half the cheddar and half the monterey jack cheese. Repeat the layers of tortillas, chicken mixture, and cheeses once.

Step 4

Cover with foil and bake for 30 minutes, then uncover and bake until bubbling and golden, 15 to 20 minutes more.

Step 5

Allow to sit 5 minutes before serving.