Flatten chicken to 1/4-in. thickness; set aside. In a shallow bowl, combine cornstarch, cumin, garlic powder, salt and cayenne. In another shallow bowl, beat egg and water. Dip chicken into egg, then roll in the cornstarch mixture and cornmeal.
In a large skillet, cook chicken over medium heat in oil until golden brown on both sides. Place in a greased 13x9-in. baking dish; arrange avocado evenly on top.
Bake, uncovered, at 350° for 10-15 minutes or until chicken juices run clear. Sprinkle with cheese. Serve with sour cream, salsa and green onions if desired.