New and Improved Carrot Cake

3/4 cup unsweetened applesauce1 pound good-quality carrots, grated fine (about 4 cups), see note 3/4 cup granulated sugar2 cups all-purpose flour (unbleached, preferred)2 teaspoons baking powder1 teaspoon baking soda 1/4 teaspoon salt 1/2 teaspoon ground nutmeg 1/2 teaspoon ground cinnamon 1/2 cup unsalted butter (or no trans fat margarine, do not use fat-free or fat-reduced), at room temperature 3/4 cup dark brown sugar2 large eggs2 large egg whites1 teaspoon vanilla extract 1/2 teaspoon coconut extract1 cup golden raisinsLower Fat Cream Cheese Frosting, recipePlace the oven rack in the lower-middle position and heat oven to 350 degrees. Lightly coat a 13-by-9-inch pan with a vegetable oil and flour spray.Place a wire mesh strainer over a bowl deep enough to keep the bottom of the strainer from touching the bottom of the bowl. Add applesauce to the strainer. Set aside.In a medium mixing bowl, toss the grated carrots with the granulated sugar. Place the carrots in a colander and place the colander in a bowl deep enough to keep the bottom of the colander from touching the bottom of the bowl; drain for 20 minutes, until about 2/3 cup liquid accumulates.Add flour, baking powder, baking soda, salt, nutmeg and cinnamon to a medium mixing bowl and whisk together until combined, about 20 seconds. Set aside.Add the butter to the large mixing bowl of an electric stand mixer and mix on medium-high speed for 4 minutes. Measure and add 1/2 cup drained applesauce; mix 2 minutes. Add the brown sugar, vanilla and coconut extract and mix for 4 minutes.Reduce the speed to medium and add the eggs and egg whites, one at a time; mixing for 20 seconds each. (The batter appears curdled at this point; do not be concerned.)Scrape down the bowl, add the drained carrots (do not squeeze them dry) and raisins and mix at medium-low speed until combined, about 15 seconds. Add the flour mixture and at the lowest speed mix until moistened, about 15 seconds.Using a rubber spatula, scrape down the sides of the mixing bowl, fold and stir the batter making certain it is well-combined and scrape into the prepared pan; smoothing out the top. Bake 35 minutes or until a toothpick inserted into the cake's center comes out clean. Allow the cake to cool completely, about 2 hours. Frost with Lower Fat Cream Cheese Frosting.Serves 16.Cook's notes: A food processor quickly grates the carrots. Cake keeps best covered and refrigerated.Nutrition values per serving, frosted: 299 calories (30 percent from fat), 10 g fat (5.8 g saturated fat), 46.6 g carbohydrates, 1.8 g fiber, 7.1 g protein, 55 mg cholesterol, 294 mg sodium.