In a large bowl, beat the cream cheese, onions, 1-1/2 cups Mexican-cheese blend, garlic, 1/4 teaspoon cumin and cilantro until blended. Stir in chicken; set aside.
In a large saucepan, melt butter. Stir in flour until smooth; gradually add broth. Bring to a boil; cook and stir for 2 minutes or until thickened. Remove from the heat. Stir in Monterey Jack cheese, sour cream, chilies, thyme, salt, pepper and remaining cumin.
Spread 1/2 cup of the cheese sauce in a greased 13-in. x 9-in. baking dish. Top with six tortilla halves, a third of the chicken mixture and a fourth of the cheese sauce. Repeat tortilla, chicken and cheese sauce layers twice. Top with remaining tortillas, cheese sauce and Mexican cheese.
Cover and bake at 350° for 30 minutes. Uncover; bake 10 minutes longer or until heated through. Let stand 5 minutes before cutting. Yield: 12 servings.