Heat oven to 375°F. Coat 12-cup standard-size muffin pan with nonstick cooking spray.
Mix flours, soda, cinnamon, salt, cloves and nuts in bowl.
Beat egg and sugar in medium-size bowl. Add oil, vanilla and applesauce.
Make well in center of flour mixture. Add egg mixture to well. Stir until flour mixture is evenly moistened and batter comes together. Fold in carrots and raisins. Spoon 1/3 cup batter into each cup.
Bake in 375°F oven 20 minutes, until pick inserted in centers comes out clean. Let cool in pan on rack 2 minutes. Turn out on rack; cool.
Serve muffins warm or at room temperature with spread.
Beat together cheese and butter in small bowl until smooth. Beat in vanilla. Gradually beat in sugar until fluffy.