Preheat the oven to 180° C and line a tray with parchment paper.
Place cocoa powder, sugar and flour in a medium mixing bowl, and add the chilled butter.
With your palms facing upwards, use your fingertips to rub in the butter until the mixture resembles sand. Add the egg, mix and knead well on a lightly floured, cool benchtop.
Shape the pastry into a disc, wrap well in cling film and place in the fridge for 1 hr to rest.
On a piece of parchment paper, roll the dough to a thickness of 3 mm, then cut out the cookies.
Place the cookies in the prepared tray and cook for 10-15 minutes.
Store in a tin box or an airtight container.