Carrot Cupcakes with Cream-Cheese Icing

I wanted to have some sort of carrot cake here and felt that this cupcake version was the right one. I know carrot muffins have long been in existence but I wanted something luscious and sweet and treaty: a cake not a breakfast scourge. For a reason I cannot quite fathom, these seem to go down particularly well if I bring them out after fish.