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Preheat oven to 350°F. For the Cake, grease and flour 2 (9-inch) round cake pans. Set aside. Mix flour, granulated sugar, baking soda, salt, cinnamon and allspice in large bowl with spoon. Add oil, applesauce, eggs and vanilla; mix well. Add carrots and walnuts; mix until well blended. Pour batter into prepared pans.
Bake 40 to 45 minutes or until toothpick inserted in center comes out clean. Cool in pan 10 minutes. Remove from pans; cool completely on wire rack.
For the Frosting, beat cream cheese, mascarpone cheese, butter and vanilla in large bowl until light and fluffy. Gradually beat in confectioners' sugar and nutmeg until smooth. Fill and frost cooled cake with frosting.