In a large heavy saucepan, cook the mushrooms in the butter over moderate heat, stirring, until most of the liquid they give off has evaporated. Remove mushrooms and set aside in a small bowl. Add another tablespoon of butter if needed, then stir in the flour, and cook the mixture over low heat, stirring, for 3 minutes. Add the milk, broth, and wine in a stream, turn up the heat, and bring the mixture to a boil, stirring constantly. Lower the heat and simmer the sauce for 5 minutes. Add vanilla, stir well, and turn off heat.

In the meantime, cook the pasta in salted water until it is al dente and drain it well.

In a large bowl combine the pasta, mushrooms, sauce, chicken, peas, and salt and pepper to taste, and mix well. Stir in 1/2 cup of the Parmesan, and transfer the mixture to a buttered shallow 3-quart casserole. Sprinkle top with balance of Parmesan cheese.