Preheat oven to 170C (150C fan, gas mark 3). Place 12 cake cases on a bun/cake tray.
Whisk together the vegetable oil, caster sugar, egg, yoghurt and courgette in a large bowl. Add the flour and cocoa powder and stir until the mix is just combined – there should be no flour visible but it should still be lumpy.
Divide the mix evenly between your 12 cases and bake for 15-20 minutes, or until springy when pushed. Leave to cool on cooling rack.
While they cool, make the icing. Blitz the icing sugar, cream cheese and butter together in a food processor – or you can do it by hand – until smooth and glossy. You must get rid of all lumps.
For an extra finishing touch, you can turn these into butterfly cakes. Cut a dome from the top of each cupcake and fill divot with icing. Half the cut-out piece to create “wings” and place on top of each cake. Dust with icing sugar to finish.