In a large skillet, cook mushrooms in butter until tender. Stir in flour; gradually add the chicken broth. Bring to a boil. Cook and stir for 2 minutes or until thickened. Remove from the heat; stir in the cream, parsley, salt, nutmeg, pepper, and wine if desired. Fold in the chicken and spaghetti.
Turn into a greased 3-qt. baking dish; sprinkle with Parmesan cheese. Bake, uncovered, at 350° for 30 minutes or until heated through.