Bring a large pot of water to a boil, add salt and noodles. Cook for 7-8 minutes until tender. Drain, drain cold water to prevent sticking, and set aside. On medium skillet, heat the oil and fry the chicken until fully cooked, add the broccoli, onion and garlic and cook until the onions are translucent. Removing from fire & set apart . In other saucepan, melt the butter & beat in flour. Cook for 1 minute, add chicken broth and milk and whisk until sauce begins to thicken. Cook until the sauce tightly coats the back of the spoon. Remove from heat and add basil, salt, Parmesan cheese and 1/4 C of mozzarella cheese.
Add the chicken mixture to the sauce and mix well. Assemble them… In a lightly greased 9″ x 13 pan”, place a layer of noodles, put a good layer of the sauce mixture on top and sprinkle with a quarter of the remaining cheese. Repeat for a second layer ending with a topping of noodles, then pour any remaining sauce on top and sprinkle with the remaining cheese. Bake at 375 degrees for 30 minutes or until golden brown and bubbling.