Standard icing for carrot cake is philadelphia cream cheese icing. If store bought or restaurant served you have to scrape it off, If homemade, what would you choose? I am not a "crisco" icing fan, popular with the cake decorating teams. My go-to icing is buttercream. But I am open to new ideas.
As a side note, my carrot cake is made with whole wheat flour, ground from wheat berries so the germ and bran is included. This holds the moisture, and gets more moist each day. This wheat combo adds another level of nuttiness to the cake and takes any baking recipe over the top!