Preheat the oven to 180C/350F/Gas 4 and line the pockets of a muffin tray with muffin cases.
Beat the sugar, oil and eggs in mixing bowl until smooth, then stir in the grated carrot and, if you like, up to 150g/5½oz chopped nuts, dried fruit, or a mixture of both.
In a separate bowl combine the flour, baking powder, spices and cocoa so that they're evenly mixed, then tip this into the carrot mixture and stir well.
Fill the muffin papers to about two-thirds full, then bake for about 25 minutes, or until a skewer poked in comes out almost clean.
For the frosting, make sure the butter is soft, then, using a whisk or electric mixer, beat it with the cream cheese in a bowl until smooth and light.
Stir in the icing sugar with a spoon until it begins to come together, then whisk again briefly until light and smooth. Pipe or spoon blobs of the frosting on each cold cupcake. Decorate with sugar-paste carrots or, say for Easter, with mini chocolate Easter eggs.