Mix the delicious flavor of cheesecake with a rich carrot cake. Cook this Carrot Cake without Oil Filled with Cheesecake, a sweet dessert that you will love. The carrot cake, with cream cheese frosting, pairs very well with cheesecake. For this Carrot Cake without Oil Filled with Cheesecake, we do not use oil; the fat from the egg and butter is enough to give the cake a moist feel. Had you thought of combining these two desserts?