Place the sugar, butter, flour and vanilla bean paste into a food processor. Pulse until a dough forms.
Weigh the dough and divide it in half evenly.
Knead the cocoa powder into one half of the cookie dough until no streaks of vanilla dough remains.
Divide the vanilla dough into two equal balls. Form each ball into a square log (use a bench scraper/clean metal ruler to really square off the edges), about 1 x 1 x 17cm. Set aside, then repeat with the chocolate dough, so that you have four logs. Do not add any extra flour/cocoa powder at this stage— you need the dough to be slightly sticky.
Press one vanilla log against one chocolate log. Place the second vanilla log on top of the first chocolate log, then the second chocolate log in the remaining space, on top of the first vanilla log. Press the logs together gently so they stick.
Wrap the log tightly in cling film and use a bench scraper to press up against the sides and make it super square. Place the log into the fridge to chill for 2 hours before slicing and baking.
Preheat the oven to 180°C (conventional, not fan).
Cut the log into approx. 5-7mm slices. Space the cookies on lined baking trays and bake in the preheated oven for 6-8 minutes, until just starting to turn golden around the edges.
Allow the cookies to cool for 5 minutes on the trays, then transfer to a wire rack to cool completely before enjoying. The cookies can be kept in an airtight container at room temperature for about 3 days before they start going soft.