Preheat oven to 350. Cook pasta according to package. Drain and set aside.Run cold water over broccoli to thaw.
In a large saucepan melt butter. Stir in flour, basil, salt, and pepper. Add milk all at once cook and stir until bubbly. Cook and stir for one more minute. Remove from heat and stir in chicken 1/2 cup parmesan cheese and well drained broccoli. Add pasta toss to coat.
Place chicken mixture in greased 7x12 baking dish. Cover with foil and bake at 350 for 20 minutes. Remove foil add rest of cheese bake for another 10 or until heated through.