First, prepare your carrots by washing and peeling them. Then, grate them using the medium-sized holes on a box grater until they resemble finely shredded cheese. Measure out 2 cups of grated carrots into a bowl and set aside.
Next, preheat your oven to 350F and grease 3 round 6" cake pans or 2-3 round 8" cake pans. Line the bottom of each pan with a round sheet of parchment paper.
In a separate bowl, whisk together the flour, baking soda, salt, cinnamon, nutmeg, and clove. In a large bowl, whisk together the oil and sugars until combined. Mix in the eggs, vanilla, and sour cream. Fold in the dry ingredients and carrots, making sure to mix until just combined.
Evenly distribute the batter between the prepared cake pans and bake for 20-25 minutes or until a toothpick inserted in the center comes out with a few moist crumbs. Let the cakes cool in the pan for 20 minutes before turning them out onto a cooling rack to cool for an additional 30 minutes.
While the cake is chilling, prepare the cream cheese frosting.
In a pan over medium heat, melt the butter until golden brown. Transfer the melted butter into a bowl and put in the fridge until it turns back into a solid.
Add the butter and cream cheese into a mixing bowl with a paddle attachment and whip for 3-5 minutes until it is light and fluffy.
Slowly add in the powdered sugar until combined. Add in the vanilla and whip until smooth.
To assemble the cake, level off the tops of each cake layer using a cake level. Then, spread a thin and even layer of frosting between each layer.
Apply a thick layer of frosting around the cake and spread it evenly. You can use any remaining frosting to pipe swirls on top of the cake and add carrot decorations all around the outside.
To make the carrot decorations, separate a few spoonfuls of frosting into two dishes. To one dish, add green food coloring. To the other dish, add orange food coloring. Transfer each colored frosting to a piping bag fitted with a small round tip and pipe tiny carrots all around the outside of the cake, followed by the green carrot stalks.
Best served slightly chilled!