Preheat the oven to Gas 4, 180°C, fan160°C. Put 12 paper muffin cases in the holes of a muffin tray.
Grate carrots into a large bowl, add all the remaining ingredients and beat well with a wooden spoon until just mixed - don't over-mix or the muffins will be tough.
Spoon mixture into paper cases. They will be almost full. Bake for about 25 minutes until just firm.
To make the icing, beat the butter and icing sugar together until smooth then beat in the cream cheese. Spread icing onto the cakes. Roll orange marzipan into small carrot shapes and mark with a knife to make them look realistic. Make little green leaves with marzipan and place with the carrots onto the cupcakes.
The cakes will keep without icing for 3-4 days in a cake tin. When iced, store in the fridge for 1-2 days.
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