Add the softened butter and sugar to a large bowl or the bowl of a stand mixer, and beat with a hand mixer or stand mixer until creamy and light. Add the egg and mix briefly, just until combined.

In a separate bowl, whisk together the all-purpose flour, vanilla, baking powder, and cocoa powder until fully combined. Add the all-purpose flour mixture to the wet dough a little at a time, mixing as you go. The dough will be fairly dry.

Divide the dough into 4-6 portions and roll out each one on a lightly floured surface. The dough should be about 1/2 cm thick. Dust with plenty of all-purpose flour and lift the dough occasionally as you roll to make sure it doesn't stick to the counter. You can also run a flat spatula underneath the dough after rolling to loosen it.

Cut out cookies using cookie cutters. Place the cut-out cookies on baking sheets lined with parchment paper. They can be placed close together, since the cookies won't spread.

Bake the cookies at 180°C for 6-8 minutes, until firm and lightly crisp. Let them cool completely on a wire rack.

Make the icing by stirring the powdered sugar into the egg white. Adjust the consistency so it's pipeable - the icing is ready when a peak drizzled on top takes 5-10 seconds to melt back into the rest of the icing.

Transfer the icing to a piping bag fitted with a tip and decorate the cookies.