Preheat oven to 350F. Grease 8-inch square pan with 2-inch-high sides. Combine first 5 ingredients in large bowl. Add oil, egg whites and vanilla and blend. Stir in walnuts. Transfer to prepared pan. Bake until brownies are slightly puffed in center and edges are beginning to brown, about 30 minutes. Cover hot brownies in pan with foil and chill overnight. Cut brownies into 16 2-inch squares. (Can be prepared 3 days ahead. Store in airtight container.)
