Preheat the oven to 200C/400F/Gas 6. Line a 12-hole muffin tin with paper cases.
Sift the cocoa powder, flour, baking powder and sugar into a bowl.
Blend the eggs, beetroot, stout and oil in a food processor until smooth.
Stir the beetroot into the flour mixture until just combined (do not overmix).
Spoon the mixture into the muffin cases and cook in the oven for 20-25 minutes, or until the cupcakes have risen and the tops are springy to the touch. Remove from the oven and set aside to cool.
For the cream cheese icing, beat the butter, cream cheese and vanilla together in a bowl until smooth; then slowly beat in the icing sugar.
Spread the icing onto the muffins with a knife or spoon the icing into a piping bag fitted with a 1cm/½in star nozzle and pipe the icing onto the muffins.
