Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x13 inch baking dish.
Remove stems from mushrooms. Finely chop stems and set aside. Arrange caps hollow side up in the baking dish. Drizzle with 5 tablespoons melted butter, and salt and pepper to taste. Melt 1/4 cup butter in a medium saucepan over medium heat. Stir in the mushroom stems and onions, and cook 5 minutes, or until tender. Gradually blend in flour and heavy cream until smooth. Remove from heat. Mix in parsley. Generously stuff mushroom caps with the mixture. Top with Swiss cheese. Bake 15 to 20 minutes in the preheated oven, or until lightly browned.