Preheat oven to 325°F. Butter three 9x2-inch round cake pans, flour the insides, and tap out the excess. Set aside.

Whisk the flour, baking powder, baking soda, cinnamon and salt in a medium bowl. In another bowl, stir together the carrots, chopped nuts, coconut, and raisins. Set aside.

Working with a stand mixer, beat the sugar and oil together on medium speed until smooth. Add the eggs one by one, beating after each addition until smooth. Reduce the speed to low and add the flour mixture, mixing only until just combined. Fold in the carrot mixture. Divide the batter evenly among the baking pans.

Bake for 40-50 minutes, rotating the pans just past the midway point, until a toothpick inserted into the centers comes out clean. Cool for about 10 minutes, then run a knife around the sides of the cakes. Remove the cakes from the pans; place back on cooling racks and cool completely.

The cakes can be wrapped airtight and kept at room temperature overnight or frozen for up to 2 months.

Divide the cream cheese frosting in half. Stir ½ cup of coconut into one half of the frosting for filling the cake.

Place one layer of the cake right-side up on a cardboard cake round or a cake plate. Tuck strips of parchment under the edges of the cake to protect the plate while frosting.

If using the coconut filling, top the layer with half of the coconut frosting. Use an offset spatula to smooth the frosting all the way to the edges.

Place a second layer of cake upside down on top of the first layer. Top with the remaining coconut frosting or another portion of plain frosting, spreading to the edges.

Place the final layer right-side up on top of the previous layers. Use the rest of the frosting to cover the top and sides of the cake. If desired, decorate with toasted nuts or toasted coconut.

Chill the cake for 30 minutes to set the frosting before serving.