In another large heavy saucepan, bring milk and 1cup of broth to a boil.
Stir in polenta; cook 4 minutes, stirring constantly.
Stir in half of cheese and salt.
Divide polenta among 4 gratin dishes; top with remaining cheese.
Broil 5 minutes in the oven set on 'broil'.
Top each serving with sautéed mushrooms.