Remove stems from mushrooms and set aside for another use. Cook mushroom caps in a small amount of boiling water in a covered saucepan for 6 to 8 minutes or until softened. Drain and invert caps on paper towels.
Brush one phyllo sheet with melted butter. Top with second sheet; brush with melted butter. Layer with remaining phyllo and melted butter. Cut phyllo stack lengthwise into thirds; cut each third crosswise into four squares, making 12 squares total.
Place a mushroom on each phyllo square; top each mushroom with about 1 teaspoon of the cheese and about 1 teaspoon of the walnuts. Bring corners of phyllo together on top of mushrooms and pinch to seal. Place on an ungreased baking sheet. Brush with remaining melted butter. Bake in a 400 degree F oven for 11 to 13 minutes or until pastry is golden. Serve warm. Makes 12.