Preheat oven to 350 degrees. Coat 11 by 7 by 2-inch baking dish with nonstick cooking spray and set aside. Sauce: Melt butter in medium heavy skillet over moderate heat. Add garlic, red pepper, and cumin and stir-fry 1 minute. Blend in flour, add broth and milk, and cook, stirring constantly, until thickened and smooth - about 3 minutes. Stir in sour cream, salt, and black pepper to taste; set aside. Filling: Melt butter in large heavy skillet, over moderate heat. Add onion, green pepper, green chilies, mushrooms, tomatoes, and pimiento, and cook, stirring often, until vegetables soften and flavors meld-10 to 15 minutes. Tortillas: Pour oil to depth of 1/2 inch in small heavy skillet, set over moderate heat, and heat until ripples appear on skillet bottom. Holding tortillas by tongs, dip one by one into oil just long enough to soften, 5 to 10 seconds. Drain on paper towels.
To Layer: Arrange half of tortillas in bottom of prepared baking dish, then build up layers this way, distributing each evenly: 1/2 chicken and 1/3 sauce; 1/2 each filling, cheese, olives, and scallions, and 1/2 remaining tortillas, chicken, filling, cheese, olives, scallions, and finally, remaining sauce. Bake, uncovered, until bubbly- about 30 to 35 minutes. Serve at once.
Recipe adapted from American century