Preheat oven to 350 degrees. Grease three 6-inch cake pans or two 9-inch cake pans generously with butter or oil.
Before you start, be sure all of your filling components are grated and chopped to a fine consistency. Meaning, shred the carrots on the smallest setting of your grater, chop the pecans and the coconut into small pieces. I find it helpful to perform the latter in a food processor. They don't have to be crumbs, just smaller bits that will conform much more easily to the cake batter.
Okay, now that the disclaimer is said, let's start! In the bowl, whip the coconut oil and sugars with a stand or hand mixer for 1 minute until incorporated. Add the vanilla extract and buttermilk/milk and mix to a creamy consistency. Crack eggs one and a time - whip until fully blended in before adding the next egg.
In a separate small bowl, sift together the flour, baking powder, baking soda, cinnamon, ginger, clove, orange zest, and salt. In three turns, pour dry ingredients into the wet, whizzing just enough to leave only a few streaks of flour before adding the next batch. With a spatula, fold in the carrots, pecans, and coconut.
Pour batter evenly into the three cake pans. Bake in the oven for 35-40 minutes until a toothpick inserted into the center removes clean with just a few moist crumbs. Cool in the pans for 15 minutes, then run a knife around the edges and flip onto a wire baking rack to cool completely.
When the cake layers are cool, prepare the frosting. Whip together the cream cheese, butter, powdered sugar, vanilla, orange zest, and orange juice (use just one tablespoon at a time here) until creamy and spreadable. I used about 3 tablespoons of juice, but you may need more or less.
If needed, level the cakes with a serrated knife to create flat tops for stacking. Set one cake layer on a plate or cake stand. Frost the top evenly, then stack a second layer. Frost the second layer, then finish with the third. Begin frosting a thin layer of buttercream all over the cake - this is your crumb layer. Set in the fridge for about 10 minutes to let the buttercream solidify just a bit. Once done, remove from the fridge and continue frosting until the whole cake is thoroughly covered. Garnish with carrot tops and additional pecans, as desired. You can pipe little carrots all over the cake if you wish as well!