For the Cake:
2 cups all-purpose flour
2 teaspoons baking powder
2 teaspoons baking soda
2 teaspoons ground cinnamon
1 teaspoon ground cloves
1 teaspoon ground nutmeg
1 teaspoon ground allspice
¾ teaspoon salt
3 cups grated carrots
1 cup coarsely chopped walnuts
1 cup shredded coconut (sweetened or unsweetened)
½ cup raisins
2 cups granulated sugar
1 cup canola oil
For the Frosting:
8 ounces cream cheese, at room temperature
4 ounces (½ cup) unsalted butter, at room temperature
1 pound (3¾ cups) powdered sugar
1 tablespoon vanilla extract
Position the racks in the oven into thirds and preheat the oven to 325 degrees F. Grease and flour three 9×2-inch round cake pans. Put two pans on one baking sheet and one on another.
Whisk together the flour, baking powder, baking soda, cinnamon, cloves, nutmeg, allspice and salt. In another bowl, stir together the carrots, chopped nuts, coconut and raisins.
In the bowl of a stand mixer fitted with a paddle attachment, beat the sugar and oil together on medium speed until smooth. Add the eggs one by one, and continue to beat until the batter is even smoother. Reduce the speed to low and add the flour mixture, mixing only until the dry ingredients disappear. Gently mix in the chunky ingredients. Divide the batter among the three baking pans.
Bake for 40 to 50 minutes, rotating the pans from top to bottom and front to back at the midway point, until a thin knife inserted into the centers comes out clean; the cakes will have just started to come away from the sides of the pans. Transfer the cakes to cooling racks and cool for about 5 minutes, then run a knife around the sides of the cakes and unmold them. Invert and cool to room temperature right side up. (The cakes can be wrapped airtight and kept at room temperature overnight or frozen for up to 2 months.)
To make the frosting: Beat the cream cheese and butter together until smooth and creamy. Gradually add the sugar and continue to beat until the frosting is velvety smooth. Beat in the vanilla extract until well-combined.
To assemble, stack the layers, spreading a generous amount of frosting between layers and then cover the top and sides. Garnish and refrigerate for at least 30 minutes before serving.