Preheat the oven to 350. Line two 8 inch cake pans with parchment, spray with cooking spray, and set aside.

In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, salt, and allspice, and set aside. In a large bowl or the bowl of a stand mixer, mix together the sugar, brown sugar, eggs, oil, sour cream, and vanilla until well blended. Add the dry ingredients to the wet ingredients and mix until just combined. Fold in the shredded carrots.

Pour the batter into the prepared pans, dividing evenly. Bake 35-40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool completely before frosting.

To make the frosting, in a large bowl or the bowl of a stand mixer, beat together the cream cheese and butter until light and fluffy. Add the powdered sugar and vanilla and mix until smooth. Add a small amount of half and half to the mixture and beat until light and fluffy.

Level the cooled cake layers using a serrated knife or cake leveler. Place one layer on a cake turntable or large platter, and add a thick layer of frosting on top. Add the other cake layer, being sure to line up the edges evenly. Frost the sides and top of the cake, and decorate as desired.