1. Remove and chop mushroom stems. In a medium skillet, heat oil and butter. Add mushroom caps and 2 tablespoons wine and cook until mushrooms are soft, about 2 minutes per side. Transfer mushroom caps to an 8x8-inch baking pan. Add shallots to skillet and cook over medium-low heat, 5 minutes. Stir in garlic and cook 1 minute more. Add chopped mushroom stems, remaining wine, walnuts, bread crumbs, and salt. Mix well.
2. Heat broiler. Evenly divide stuffing among mushroom caps. Broil 6 inches from heat source until golden and heated through, about 2 minutes. Makes 2 servings.