In a bowl, combine the butter, powdered sugar, and vanilla extract. Add 1 egg and sift in the flour.
Cover with plastic wrap and refrigerate for 1 hour.
In another bowl, combine the butter, powdered sugar, and egg, and sift in the flour and cocoa powder.
Cover with plastic wrap and refrigerate for 1 hour. Roll out each piece of dough, cut it into strips, and fold it into a checkerboard pattern. Refrigerate for another hour and cut into slices. Bake at 170°C (340°F) for 18 minutes.