Adjust an oven rack to the middle position. Preheat oven to 350 degrees F. Grease two 9-inch round cake pans with butter. Dust with flour and set aside.

In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, cloves and salt. Set aside.

In a food processor fit with a metal blade, process granulated sugar, brown sugar and eggs until thoroughly combined, about 20 seconds. With the processor running, add the oil through the feed tube and blend until mixture is light in color, about another 20 seconds.

In a large bowl, combine the wet ingredients from the food processor, the flour mixture, and the grated carrots. Stir with a wooden spoon or rubber spatula until combined and no flour streaks remain.

Pour the batter into the two prepared cake pans (dividing the batter evenly). Bake at 350 degrees F for 35 to 40 minutes. Rotate pans halfway through the baking time. Cakes are done when a toothpick inserted in the center comes out clean. Let cakes cool completely in the pans set on a wire rack (about two hours).

In the bowl of a hand mixer (or using a hand mixer), combine cream cheese, butter and vanilla until smooth, about 30 seconds. Scrape down the sides of the bowl with a rubber spatula as needed. With the mixer on low, add the confectioners' sugar and mix until smooth.

Run a butter knife around the edge of the cake pans. Invert the cakes onto a wire rack.

Place one cake on a cake stand and drop a large dollop of frosting in the center. Use an offset spatula to push the frosting toward the edges of the cake evenly. Place second cake on top of the frosted bottom cake.

Create the crumb coat*. Spread a thin layer of frosting over the top and sides of the cake. It's okay if you see the cake and crumbs at this step. Chill the cake for 10 to 15 minutes for the crumb coat to set.

Apply a second, thicker layer of frosting. Cut and serve the cake!