When I was growing up there was only one cake. It was carrot cake, because red velvet's invasion of the American bakery world hadn't happened yet and this was the only cream cheese frosting delivery vehicle around.
Think about it: in the American frosting world—that is, discounting Swiss buttercream and its relatives—what's a better frosting than cream cheese? You need to whip cream pretty heavily or stabilize it to keep it in shape, and I'm not alone in thinking that American buttercream is just too thick and sweet for most cakes. (Do you agree? Let me know.)
These days I keep my moist spice cakes and my thick frosting separate, but I haven't lost the taste for tangy dairy mixed with sweet spices and brown sugar. Anna recently showed you a carrot cake reimagined with slices of cake sandwiching a cream cheese semifreddo; here's another interpretation—carrot cake ice cream.
It's an easy blended cream cheese base flavored with turbinado sugar* and a hint of cloves. The carrots and sugar give the ice cream a complex caramel profile cut just enough by cream cheese twang. It tastes a lot like a carrot cake blitzed in a blender—in a good way.
* Also known as "sugar in the raw" and my preferred brown sugar for most ice cream. It's less molasses-y and overbearing than commercial brown sugar.
Except for frying some carrots in butter, this recipe has no cooking at all. No eggs, no tempering, no lengthy chill-downs in the fridge. Which means that you could whip this up by lunch and have it ready to eat at dinner. Piece of...you know.