Preheat the oven to 350°F. Spray a 12x7-inch baking dish with nonstick spray.
In a large skillet over medium heat, melt the butter and add onion and garlic; cook, stirring occasionally, for 2 to 3 minutes until softened and golden. Add the mushrooms, cayenne and cumin and cook, stirring often, for 6 to 8 minutes until the mushrooms are tender and release their juices.
Blend in the flour and cook and stir for 1 minute. Add the broth, milk, sour cream, salt and black pepper and cook, stirring constantly, about 3 minutes until thickened.
Cover the bottom of the prepared dish with 4 tortillas, then layer the remaining ingredients in the dish this way: ½ diced chicken, ⅓ mushroom mixture, ½ salsa, ½ cheese, then ⅓ of the remaining mushroom mixture, then the remaining tortillas, chicken, salsa, cheese, and finish with the remaining mushroom mixture.
Bake, uncovered, for 30 to 35 minutes until bubbling and lightly browned.