Preheat oven to 350°.
Coat a large nonstick skillet with cooking spray; place over medium heat until hot. Add chicken; cook 6 minutes on each side or until done. Remove chicken from skillet; let cool. Shred chicken with 2 forks; set aside.
Recoat skillet with cooking spray; place over medium heat. Add onion and garlic; sauté 5 minutes or until tender. Add shredded chicken, beer, red pepper, and tomatoes; cook 10 minutes or until most of liquid evaporates. Remove from heat. Reserve 1 tablespoon green onions and 1 tablespoon olives for garnish. Stir remaining green onions, remaining olives, and chiles into chicken mixture; set aside.
Combine flour, salt, cumin, and coriander in a medium saucepan. Gradually add milk, stirring with a whisk until blended. Place over medium heat; cook 7 minutes or until thick, stirring constantly. Gradually add hot milk mixture to egg whites, stirring constantly with whisk. Set aside.
Place cheeses in a bowl; toss well. Set aside.
Spread 1/2 cup white sauce in bottom of a 2 1/2-quart round casserole or soufflé dish coated with cooking spray. Arrange 4 tortilla halves over sauce; top with 2 cups chicken mixture, 1/2 cup white sauce, and 1/2 cup cheese mixture. Repeat layers twice, ending with sauce. Set remaining 1/2 cup cheese mixture aside.
Bake, uncovered, at 350° for 40 minutes or until hot. Sprinkle with remaining 1/2 cup cheese mixture, reserved green onions, and reserved olives; bake an additional 5 minutes. Let stand 10 minutes before serving. Serve with sour cream and salsa.
NOTE: You can assemble the casserole ahead of time; cover and chill in the refrigerator overnight, then bake at 350º for 1 hours or until bubbly. Or freeze casserole, thaw in refrigerator 24 hours, then bake for 1 hour or until thoroughly heated.