Preheat the oven to 325 degrees F, mist three 6-inch diameter cake pans* with non-stick spray, and line with circles cut from parchment. Place the butter and brown sugar in the bowl of an electric mixer, and whip on medium-high speed (scraping the bottom and sides of the bowl with a silicone spatula occasionally) until pale and very fluffy ( a FULL 5 to 8 minutes).
Mix in the eggs, one at a time, stopping to scrape the bottom and sides of the bowl with a silicone spatula after each addition.
Stir in the vanilla until well-blended.
Stir in the all-purpose flour, cake flour, cinnamon, baking powder, baking soda, salt, nutmeg, and cloves on medium-low speed, until just barely combined (there should still be streaks of flour).
Fold in the carrots, pineapple, and walnuts, and transfer the batter to the prepared pans.
Bake until the cakes feel springy and a toothpick inserted in the thickest part comes out clean or with a few moist crumbs (about 42 to 48 minutes).
Cool for 20 minutes in the pans, then invert onto a wire rack to cool completely.
When completely cool, fill and ice with cream cheese frosting.