Place the flour and sugar into a food processor and pulse until blended. If you use granulated sugar, firstly pour the sugar only into a blender or food processor. Blend the sugar until it is a fine.
Add the butter and pulse until sandy. Then add the egg and the vanilla extract. Pulse until the mixture until a dough forms. Scraping down sides as needed.
Take the dough out. Then knead and form into a ball.
Divide the dough in half, and place one of the dough in a bow. Add the cocoa powder and well combine with hands.
Pat the plain dough into rectangle shape. And put the dough between 2 pieces of parchment paper and roll out the dough to 5 mm (3/16-inch) thick. Repeat with the remaining cocoa dough.
Wrap the 2 sheets of dough in plastic wrap. And refrigerate for 1 hour.
Preheat the oven to 160 C / 325 F / gas mark 3.
Line 2 baking sheets with parchment paper. Cut the dough with a knife or cookie cutters into desired shapes and arrange on the prepared baking sheets.
Bake for 17 to 20 minutes until edge of the cookies slightly brown. Then cool on the baking sheet until firm.