1. Prepare the cake. Preheat oven to 325 degrees. Spray two 9-inch round cake pans with vegetable cooking spray. Line the bottoms with parchment paper and spray the paper.
2. Sift together both flours, baking soda, cinnamon, cloves, nutmeg, and salt into a large bowl. Stir in sugar. Add applesauce and use an electric mixer on low to blend until mixture looks crumbly.
3. In a small bowl, lightly whisk together egg whites, whole egg, and vanilla. Add to flour mixture and mix on medium speed until smoothly blended, about 30 seconds. Stir in carrots and nuts. Batter will be thick.
4. Divide batter evenly between cake pans. Bake just until a toothpick inserted in center of a cake comes out clean and tops are golden, about 28 to 32 minutes.
5. Cool pans on a wire rack for 10 minutes, and then run a knife around the edges of the cakes to loosen. Invert each onto the wire rack. Discard paper liners. Turn cakes right side up and cool completely, about 1 hour.
6. When cakes are cool, prepare frosting. In a large bowl, use an electric mixer on medium speed to beat cream cheese, butter, and coconut and vanilla extracts until blended. Add confectioners' sugar and beat on low speed until frosting is smooth.
7. Place one cake on a serving plate. To keep the plate clean, tuck 3-inch-wide waxed paper strips an inch or so under the edges of the bottom of the cake all the way around. Spread the frosting over the top of the cake, leaving a 1/2-inch border.
8. Carefully place second cake over frosting, flat side up. Spread remainingfrosting over the top and sides of the cake. Pat nuts onto sides of the cake. Gently pull out and discard the paper strips. Cake can be covered and refrigerated for up to 2 days; let it reach room temperature before serving. Use a sharp knife to cut.
Source: Hannaford fresh Magazine, September - October 2012