Grease a springform cake tin with butter and preheat oven to 180 degrees C.
In a bowl, combine the flour, baking powder and cocoa.
Break the chocolate into small bits and melt in a bowl over a pan of simmering water. When almost melted, add espresso and stir. Add butter piece by piece, stirring until all is melted. Let cool a few minutes.
Beat the egg yolks and add to the chocolate then fold in the pureed beetroot.
Beat the egg whites until stiff and then beat in the sugar. Fold the egg whites into the chocolate mixture, then fold into the flour mixture.
Pour the batter into the prepared tin and bake on the middle rack 45-50 minutes. This is a moist cake so the skewer test should have a few crumbs. Let cool 2 hours, then sprinkle with icing sugar.