Remove stems from mushrooms and discard; set caps aside. Arrange zucchini in a vegetable steamer over boiling water in a Dutch oven. Cover and steam 5 minutes. Place zucchini on several layers of paper towels; cover with additional paper towels. Let stand 15 minutes, pressing down occasionally to remove moisture. Combine zucchini and next 6 ingredients; stir well. Spoon mixture evenly into mushroom caps. Carefully arrange mushrooms in a single layer in steamer over boiling water in pan. Cover and steam 6 minutes or until mushrooms are barely tender. Arrange mushrooms on a serving platter; sprinkle with Parmesan cheese. Serve immediately. Yield: 1 dozen appetizers (serving size: 1 stuffed mushroom).