HEAT oven to 375ºF.
COOK pasta in large saucepan as directed on package, omitting salt.
MEANWHILE, heat oil in large skillet on medium heat. Add zucchini, mushrooms and garlic; cook and stir 3 to 4 min. or until zucchini is crisp-tender. Add flour and seasonings; cook and stir 1 min. Stir in broth; cook and stir 2 to 3 min. or until thickened. Add Neufchatel; cook and stir 2 to 3 min. or until melted.
DRAIN pasta; return to pan. Add zucchini mixture, spinach, Parmesan and 1/2 cup mozzarella; mix lightly. Spoon into 2-qt. casserole sprayed with cooking spray; top with remaining mozzarella.
BAKE 10 min. or until mozzarella is melted.