Pound chicken to 1/4-inch-thickness on work surface; turn smooth sides down. Mix cream cheese, spinach, 1 cup mozzarella and 3 Tbsp. Parmesan until blended; spread onto chicken. Starting at one short end of each breast, roll up chicken tightly. Secure with wooden toothpicks, if desired.
Whisk egg in shallow dish until blended. Combine cracker crumbs and remaining Parmesan in separate shallow dish. Spray 13x9-inch baking dish with cooking spray. Dip chicken, 1 bundle at a time, into egg, then into crumb mixture, turning to evenly coat all sides with crumb mixture. Place, seam sides down, in prepared baking dish.
Bake 30 min. or until chicken is done (165ºF). About 5 min. before chicken is done, cook pasta sauce on medium-low heat until heated through, stirring occasionally.
Remove and discard toothpicks from chicken. Spoon pasta sauce over chicken; top with remaining mozzarella.