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1. Preheat the oven to 350u00b0F. Lightly spray a 13 x 9 x 2-inch baking pan with cooking spray. Sprinkle 2 tablespoons flour in the pan, shaking so the flour adheres to the sides and bottom. Shake out any excess flour.
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2. In a medium mixing bowl, using an electric mixer on medium speed, beat the egg whites, sugars, applesauce, 1/2 cup milk, the oil, and 1 1/2 teaspoons vanilla for 1 minute, or until combined.
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3. In a medium bowl, stir together the whole-wheat flour, remaining 1 1/4 cups all-purpose flour, cinnamon, baking powder, and allspice. Gradually add the flour mixture to the egg white mixture while beating on medium speed for about 1 minute, or until blended.
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4. Stir in the carrots, pineapple with liquid, and raisins. Pour into the pan, lightly smoothing the top.
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5. Bake for 35 to 40 minutes, or until a wooden toothpick inserted in the center comes out clean. Transfer to a cooling rack and let cool for at least 1 1/2 hours before frosting.
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6. In a medium mixing bowl, using an electric mixer on medium speed, beat together the frosting ingredients except the pecans for 1 minute, or until smooth. Spread on the cooled cake. Sprinkle with the pecans. Serve the same day for peak flavor and texture.
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7. Cover any leftovers and refrigerate for up to three days.
