In a large saucepan, melt 4 tablespoons butter; stir in flour until smooth. Gradually add milk and broth; bring to a boil. Boil and stir for 2 minutes. Whisk half into eggs; return all to pan. Cook and stir over low heat for about 1 minute or until mixture reaches at least 160°. Remove from heat; add 1/2 cup Parmesan, 1/2 teaspoon salt, nutmeg and cayenne. Set aside. , In a large skillet, saute onion and garlic in remaining butter until tender. Add the chicken, broccoli, carrot, parsley, pepper and remaining salt; cook for 3 minutes. Spread 1/2 cup of the Parmesan custard mixture into an ungreased 13x9-in. baking dish. , Layer with a third of the noodles, half of the chicken mixture, 1/2 cup Parmesan custard, a third of the mozzarella cheese and 1 tablespoon Parmesan cheese. Repeat layers. Top with remaining noodles, mozzarella and Parmesan custard. Sprinkle with remaining Parmesan cheese. , Bake, uncovered, at 350° for 40-45 minutes or until bubbly. Let stand 10 minutes before serving.