MAKE THE CAKE. Preheat the oven to 350-degrees and grease and flour two 8-inch round cake pans.
In a large bowl, whisk the flour, cinnamon, cloves, salt, baking soda and baking powder until well combined.
Meanwhile, in a stand mixer fitted with the paddle attachment, beat the eggs, oil, sugar, brown sugar and vanilla on medium-high until creamy, for 5 minutes.
Add the carrots and coconut and mix to combine.
Add the dry ingredients and mix on medium, just until the batter comes together.
Divide the batter evenly into the prepared cake pans and bake until a toothpick comes out clean when inserted into the center, for 30-40 minutes.
Cool the cakes for 15 minutes before flip them onto a cooling rack; cool completely.
MAKE THE FROSTING. In a stand mixer fitted with the paddle attachment, cream the cream cheese and butter over medium-high speed until light and fluffy, about 5 minutes, scraping the sides and bottom of the mixing bowl with a rubber spatula often.
Add the vanilla and confectioners sugar; mix on the lowest speed until the sugar is fully incorporated.
Increase the speed to medium-high and beat until light and fluffy, about 3 minutes.
TO ASSEMBLE, cut each cake in half to create four layers.
Place one layer, flat-side-down onto a large serving plate or cake stand.
Add 1 cup of frosting and, using an offset spatula, spread it evenly over the layer, going all the way to the edge of the cake.
Refrigerate for at least 2 hours to set. If not serving on the day it was made, loosely wrap the cake with plastic wrap; bring to room temperature for 1 hour before serving.