Cook pasta in large saucepan as directed on package, omitting salt and adding broccoli to the boiling water for the last 3 min.
Meanwhile, heat large skillet sprayed with cooking spray on medium-high heat. Add chicken and basil; cook 3 min. or until chicken is no longer pink, stirring frequently. Add flour; cook and stir 1 min. Add broth; bring to boil. Simmer on low heat 3 min. or until sauce thickens and chicken is done. Add Neufchatel; cook and stir 1 min. or until melted.
Drain pasta and broccoli; return to saucepan. Add chicken mixture; mix lightly. Stir in 1/2 cup mozzarella. Spoon into 8-inch square baking dish.
Bake 15 min. or until heated through. Sprinkle with remaining mozzarella and the Parmesan. Bake 3 min. or until cheese is melted.