Preheat oven to 350°.
Spritz a 12 x 7 1/2 inch baking dish with nonstick cooking spray; set aside.
Melt butter in a large heavy skillet over medium heat; add onion and garlic, and cook, stirring occasionally, 2-3 minutes until limp and golden.
Add mushrooms, cayenne, and cumin and cook, stirring occasionally, 6-8 minutes until mushrooms release their juices and most of these evaporate.
Blend in flour and cook and stir 1 minute ; add broth, milk mixture, salt, and black pepper and cook, stirring constantly, about 3 minutes until thickened.
Cover bottom of baking dish with 4 tortillas, then layer remaining ingredients in dish this way, each time spreading to cover layer below: half diced chicken, one-third mushroom mixture, half salsa, half cheese, then half remaining mushroom mixture, the remaining tortillas, chicken, salsa, cheese, and finish with remaining mushroom mixture.
Slide onto the middle oven rack and bake uncovered, 30-35 minutes until bubbling and tipped with brown.
Serve at once with a tartly dressed green salad; or spinach bacon salad.