1Heat oven to 325°F. Grease 13x9-inch pan with shortening or cooking spray; lightly flour. In large bowl, beat granulated sugar, brown sugar and 1/2 cup butter with electric mixer on medium speed until light and fluffy. Add eggs 1 at a time, beating well after each addition.
2In medium bowl, stir together flour, cinnamon, nutmeg and allspice. Alternately add flour mixture and applesauce to butter mixture, beating well after each addition. Stir in raisins and nuts. Spread batter in pan.
3Bake 50 to 55 minutes or until cake pulls away from sides of pan. Cool in pan on cooling rack while making icing.
4In 2-quart saucepan, heat 2 tablespoons butter and the milk over low heat just until butter is melted and milk is warm. Remove from heat. With wire whisk, beat in powdered sugar and vanilla until smooth. Spoon and spread over warm cake.