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).