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Step 1
Preheat oven to 375° and have ready a 9x13” greased baking dish. Place the halved tortillas in a shallow dish (like a pie dish), and pour over 1 cup of chicken broth. Set aside and allow to soak.
Step 2
In a large rimmed sauté pan over medium-high heat, melt together butter and olive oil. Add celery, onion, and bell pepper and sauté until softened and onions are translucent, 5-8 minutes.Add mushrooms and sauté until juices have released and they begin to take on a brown color, about 10 minutes. Add the garlic and sauté 30 seconds to a minute.
Step 3
Sprinkle over the flour and stir until a paste coats the vegetables. Slowly drizzle in the remaining 4 cups of chicken broth, whisking constantly until flour has completely dissolved and no lumps remain. Allow mixture to come to a boil, then reduce the heat to medium and allow to simmer about 5 minutes, or until the mixture has thickened.
Step 4
Stir in the tomatoes and green chilis and allow to simmer for another five minutes. Add the chili powder, cumin, salt, pepper and 2 tablespoons of cilantro. Stir once more, remove from heat and set aside.
Step 5
Combine the Cheddar and Monterrey Jack in a small bowl, and set aside.
Step 6
Spoon a thin layer of sauce on the bottom of the dish and then add a layer of tortillas. Add a layer of sauce over the tortillas, followed by a layer of chicken and then a third of the cheese mixture. Repeat with another layer of tortillas, sauce, chicken, and half of the remaining cheese.
Step 7
Add one more layer of tortillas, along with the remaining sauce, and cheese. Bake for 25-30 minutes until bubbly. Sprinkle with the remaining cilantro and set aside to cool for at least 15 minutes.