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Special Equipment: KitchenAid(R) Stand Mixer; KitchenAid(R) Sifter + Scale Attachment; Three 9-in/23-cm cake pans with 11/2-in/4-cm sides; parchment paper; food processor fitted with the medium shredding disk or a box grater; offset spatula
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Position one rack in the center and a second rack in the lower third of the oven and preheat to 350u00b0F/180u00b0C/gas 4.
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Butter three 9-in/23-cm cake pans with 11/2-in/4-cm sides. Line the bottom of each pan with a circle of parchment paper. Butter the parchment paper. Sprinkle 1 pan with a spoonful of flour, and then tilt and tap the pan to distribute the flour evenly. Turn the pan upside down over the sink and gently shake out the excess flour. Repeat with the second and third pans.
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Attach the KitchenAid(R) Sifter + Scale Attachment to your KitchenAid(R) mixer fitted with the flat beater. Place the scale lid on top. Individually weigh the carrots (10.6 oz), coconut 3 oz), walnuts (4 oz), and raisins (3 oz). Using a rubber spatula or your hands, toss them together in a medium-sized bowl until evenly combined. Set aside.
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Remove the scale lid, attach the ingredient hopper, and close the ingredient valve. Weigh the sugar (14 oz) in the ingredient hopper. Add the oil to the mixing bowl. Turn the mixer on low speed, open the ingredient valve, and sift the sugar into the mixing bowl. Beat together until smooth, about 2 minutes. Add the 4 eggs, one at a time, beating well after each addition. Turn the mixer off.
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Close the ingredient valve. Weigh the flour (8 oz), baking powder (0.28 oz), baking soda (0.42 oz), cinnamon (0.16 oz), salt (0.16 oz), and nutmeg (0.04 oz) in the ingredient hopper, taring the scale between ingredients. Turn the mixer to medium-low speed, open the ingredient valve, and sift the flour mixture into the mixing bowl. Be careful not to overmix the batter. Remove the mixer bowl, and use a rubber spatula to blend in any flour remaining on the sides of the bowl. Fold in the carrots, coconut, nuts, and raisins until evenly distributed.
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Divide the batter in three equal parts into the prepared pans, spreading evenly in each pan. Bake the cakes until they just start pulling away from the sides of the pan and a toothpick inserted into the center of a cake comes out, 40 to 50 minutes. For even baking, at the midpoint, switch the pans between the racks and rotate them front to back. Let the cakes cool in the pans on wire racks for 15 minutes. Run a table knife around the inside edge of each pan to loosen the cake sides. Invert the cakes onto the racks and peel off the parchment paper. Let cool completely before frosting. (Note: the cakes are deliciously dense; so don't expect a lot of rise once baked.)
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To make the frosting, in the stand mixer fitted the paddle attachment, beat the 16 oz (2 pkg) cream cheese on medium speed until smooth, about 3 minutes. Add the 1 cup butter and beat until combined, about 2 minutes. Turn off the mixer.
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Close the ingredient valve. Weigh the confectioners' sugar (7 oz) in the ingredient hopper. Turn the mixer to medium-low speed, open the ingredient valve, and sift the sugar into the mixing bowl. Drizzle the 1 Tbs lemon juice down the side of the mixing bowl and beat until fluffy, about 3 minutes.
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Place 1 cake layer, top side down, on a cake plate. Using an offset spatula, spread one-third of the frosting over the top. Spread the frosting right to the edge of the top without frosting the sides. Carefully set the second cake layer on top, placing it top side down and lining up the edges. Spread half of the remaining frosting on top of the layer the same way. Place the third cake layer on top, right side up. Spread the remaining frosting over the top of the cake, again without frosting the sides. Swirl the frosting to decorate the top, then garnish the top evenly with the coconut, if desired. Refrigerate the cake for at least 45 minutes to set the frosting. Remove from the refrigerator 30 to 40 minutes before serving.
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Note: Use the medium-shredding blade for your food processor, to make quick work of grating the carrots. Otherwise, use the coarse holes on a box grater.
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The frosted cake can be made up to 2 days in advance. Refrigerate until cold, then carefully cover with plastic wrap. The frosted cake also freezes well. Place it in the freezer unwrapped until both the frosting and the cake are firm and set, usually about 3 hours. Wrap the cake airtight in plastic wrap and then aluminum foil. Don't freeze baked goods any longer than 30 days, as they pick up a stale-freezer taste. Thaw the cake, still wrapped, in the refrigerator overnight. The cake will keep for 3 to 4 days.
