This straightforward recipe delivers moist, dense, and delicious carrot cake with pineapple under a cream cheese frosting. TESTED & PERFECTED RECIPE - A light and tender carrot cake with creamy vanilla cream cheese icing. Get Carrot Cake with Cream Cheese Frosting Recipe from Food Network. carrot cake recipe/soft & moist -- Cooking A Dream A pleasingly moist cake, this treat is the one I requested that my mom make each year for my birthday. It's dotted with sweet carrots and a hint of cinnamon. A delectable cream cheese frosting is the finishing touch on classic carrot cake. Fluffy cream cheese frosting makes the ultimate topper for an ultramoist and classically flavored carrot cake.