Beat the butter and sugar until light and creamy. Lightly whisk the egg with a fork in a cup, then add to the creamed butter and sugar, and beat well.
Spoon half the mixture into another bowl. Sift 70 g flour and the cocoa into one bowl and mix until well combined. Sift the remaining 100 g flour into the other bowl and add the vanilla extract. Mix until well combined. Bring each batch together into a ball of dough, wrap each one in cling film, flatten slightly and chill in the fridge for at least 30 minutes.
Between two sheets of cling film or baking paper, roll out each dough into a rectangle approx. 30 x 15cm. Place one on top of the other, trim to a neat rectangle and roll from the long edge into a log shape. Roll any trimmings into balls approx. the size of a walnut, to make marbled cookies. Wrap in some of the cling film or baking paper and chill in the fridge for at least 30 minutes, or the freezer for 5-10 minutes.
Preheat the oven to 180°C. Line one or more baking tray(s) with baking paper.
Cut the log into slices approx. 1cm thick. If they are a little flat on one side from the slicing, re-shape into a round and lay them on the tray(s), spaced about 5 cm apart. If you are making marbled cookies from the spare dough, place the balls on a lined baking tray also, and flatten slightly. You can cook all the cookies together, on a number of trays, or in batches, or keep the log in the fridge for a few days (or the freezer for up to a month) and slice and bake when needed.
Bake for 10 – 12 minutes, then leave on the tray(s) for 5 minutes before moving to a wire rack to cool completely. If baking from frozen, they will need about 5 minutes longer in the oven.