Combine broth, 1 cup onion, and next 5 ingredients (through bay leaf) in a large saucepan; bring to a boil. Reduce heat, and simmer 15 minutes or until chicken is done. Remove chicken from pan; chill 15 minutes. Reserve broth mixture for another use. Shred chicken into bite-sized pieces. Combine chicken, remaining 1/2 cup onion, and sour cream in a bowl, stirring well.
Preheat oven to 350°.
Spread 1/4 cup Green Chile Sauce in the bottom of each of 2 (11 x 7-inch) baking dishes coated with cooking spray. Warm tortillas according to package directions. Spoon about 1/3 cup chicken mixture down center of each tortilla; roll up. Place 8 filled tortillas, seam-side down, in each dish; pour 1 1/4 cups of remaining Green Chile Sauce over filled tortillas in each dish. Combine cheeses in a bowl. Sprinkle half of cheese mixture evenly over filled tortillas in each dish. Bake at 350° for 18 minutes or until thoroughly heated.