Make cake: Preheat oven to 350ºF. Butter and flour 2 8-inch round cake pans. In a bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, allspice and cloves. In another bowl, whisk sugar, oil, buttermilk and eggs. Pour oil mixture into flour mixture and stir just until evenly moistened. Fold in carrots.
Scrape batter into cake pans; smooth tops. Bake until cakes are golden brown and a toothpick inserted into center of a cake comes out clean, about 45 minutes. Let cakes cool in pans on a wire rack for 10 minutes, then invert cakes onto rack to cool completely.
Make frosting: In a bowl, with an electric mixer on high speed, beat cream cheese and butter until smooth. Add brown sugar and vanilla and beat until sugar is completely dissolved. Add confectioners' sugar and salt and beat on low speed until smooth and spreadable.
Decorate cake: Place one cake layer on a serving plate, spoon about 1 cup frosting into center, and spread with a knife or offset spatula. Place second layer on top and spread remaining frosting over top and sides.