Yes we cand aad carrot into a ice cream ..Recipes including carrots are of course nothing new and well known and used by the ancients. Some written versions do remain in the archives around the world and some are repeated in the history pages - here. These include: Lombardo Compost, Carrot Puree, pickled carrots, cariota, Jazariyyah (14thC); 16thC hereincluding puddings, carrot salad and carrot sauce.
A 10th Century Cookbook - Annals of the Caliphs’ Kitchens - Al Warraq are on aseparate page.
History of Carrot Cake here; . Ancient Carrot Puddings are here. Carrot Lemonade here. Purple Carrot powder