One of my children is a carrot cake fan. This is the fastest carrot cupcake recipe you could possibly find. We never bother with the icing but you always can mix a couple of tablespoons of philadelphia cheese with two table spoons of double cream and icing sugar and ice a little the cupcakes.
200 gr self raising flower
250 gr of grated carrots
150 ml sunflower oil
75 gr dark brown sugar
zest of one orange
one teaspoon of bicarbonate of soda
you can also add some spices if you wish: a teaspoon of cinnamon and some grated nutmeg or a teaspoon of all spice.
Mix together the flour, bicarb and orange zest (and spices if you are using them). Separately mix the oil and eggs and sugar and add it to the the flour mixture. Last add the grated carrots. Line a cupcake tray with paper cases. Put the mixture into the cases and bake in a preheated oven at 180 degrees for 20 minutes.