The more you think about carrot cake, the less it makes sense. Like the name implies, it contains carrots, yet is not “carrot-y”—their subtle flavor is overpowered by the high caramel of brown sugar, the warm embrace of cinnamon and nutmeg and clove.
We can finish this with a buttercream icing if you don't want to refrigerate or a cream cheese icing which will require refrigeration.