Start by making the vanilla dough for your biscuits. Mix the unsalted butter and sugar with a wooden spoon, then add the vanilla extract and flour. Knead until a dough is formed. Use a little water if necessary. Wrap the vanilla dough in baking parchment and chill in the fridge for at least 20 minutes.
Now it's time to make the chocolate dough. Do the same steps as for the vanilla dough; mix butter and sugar, add vanilla extract, and flour. This time put the cocoa powder as well. Knead until a dough is formed and use some water if required. Divide into two, wrap with baking parchment and chill in the fridge for at least 15 minutes.
Take out the vanilla dough and one of the chocolate dough halves from the fridge and roll open in a rectangular shape, approximately 1cm thick. Slice the dough, both vanilla and chocolate into strips of about 1cm wide, so as to have a square-shaped cross-section.
Next, alternate the dough strips by putting one strip of vanilla dough in between two strips of chocolate dough. Brush the dough strips with some egg wash so they can stick together.
Now, put one strip of chocolate dough in between two strips of vanilla dough, all on top of the other three strips prepared in the previous step. Use some egg wash in between the layers, too. Again, put one strip of vanilla dough in between two strips of chocolate dough, all three strips on top of the ones prepared just now, after putting some egg wash.
Cut the edges so as to get straight ends. Now, you should be able to see the checkerboard pattern, having nine squares of alternating vanilla and chocolate dough. Do the same alternating pattern of dough strips with the rest of your vanilla and chocolate dough. Then cut the edges as well, to get the checkerboard pattern.
Next, roll open the rest of the chocolate dough which was in the fridge. Put the long checkerboard strips on top of it, cut the extra dough from the sides, and wrap the top and bottom part of the dough to cover the checkerboard strips. Put these in the fridge for about 20 mins, while still in a cuboid shape.
Take out the cuboid-shaped biscuits dough from the fridge and slice it to form your biscuits, around 20. Put them on baking parchment and cook in a pre-heated oven for 20 minutes, gas mark 5.