Sift the dry ingredients together in a bowl. Mix together the grated carrot and the eggs in a separate bowl. Fold the dry ingredients into the carrot and egg mixture.
Mix in the chopped chocolate and lastly the melted butter. Put in a container and rest in the fridge for 45 minutes to an hour.
Preheat the oven to 180°C (350°F/Gas 4).
Take the mixture out of the fridge and spoon it into a piping (pastry) bag fitted with 12mm (1⁄2 inch) plain nozzle (tip).
Using a silicone muffin tray or cupcake tray, pipe the cake mixture into the holes until three-quarters full. You can of course also use a metal cake tin and cake cases, but I think they look more delicate without a case.
Bake for 18-20 minutes until golden brown if muffin sized or 12-15 minutes if cupcake sized. Leave to cool, then remove from the moulds.
Beat the icing sugar into the mascarpone and then add the vanilla extract. Mix thoroughly.
Place the mascarpone in a piping bag with a star shaped nozzle and pipe swirls, or you could just spread the mascarpone on top.