First make the cream cheese frosting. Mix the cream cheese, vanilla and butter together until they are completely combined. Add the powdered sugar and mix until blended. Then place it in the refrigerator to help it harden a bit. Preheat the oven to 350 degrees Fahrenheit.

Cut (3) 8-inch circles out of parchment paper and place them in the bottoms of 3 well-greased 8-inch cake pans. Set them aside.

Mix together the dry ingredients, except the nuts, in a medium-sized bowl. Set it aside. Then mix together the oil and sugars in a large bowl until well blended. Add the eggs, one at a time, beating well after each addition. Then add the coconut milk and vanilla extract and mix until blended. Add the dry ingredients to the wet ingredients and mix until they are just combined. Stir in the shredded carrots, crushed pineapple, and nuts.

Evenly distribute the cake batter between the 3 cake pans and bake them in the oven for 30 to 40 minutes or until a toothpick inserted into the cake comes out clean. Remove the cakes from the oven and allow them to cool for 10 minutes, then shake the pan slightly to loosen the grip of the cake. Allow the pans to cool for another 20 minutes before removing the cakes from the pans.

Layer and ice the cake, making sure to remove and dispose of the parchment paper. You can also garnish the top of the cake with the reserved carrot tops, if you want to. Serve immediately and refrigerate any leftovers.