Heat oven to 375 degrees F. Mix cream cheese, spinach, 1 cup mozzarella and 3 Tbsp. Parmesan until well blended; spread onto chicken breasts. Starting at one short end of each breast, roll up chicken tightly. Secure with wooden toothpicks, if desired. Set aside.
Beat egg in shallow dish. Mix remaining Parmesan and cracker crumbs in separate shallow dish. Dip chicken bundles in egg, then roll in crumb mixture. Place, seam-sides down, in 13x9-inch baking dish sprayed with cooking spray.
Bake 30 min. or until chicken is done (165 degrees F). Remove and discard toothpicks, if using. Serve topped with spaghetti sauce and remaining mozzarella.