Cut the butter into the bowl of an electric mixer. Add the sugar and cream until just combined.
Add the flours and mix until just combined
Separate the batter into two roughly equal masses. In separate bowls, mix one half of the batter with the vanilla sugar and mix the other half of the batter with the cocoa powder.
Divide each of these doughs into two roughly equal portions so that there are four separate doughs: two with vanilla sugar and two with cocoa powder.
Shape each piece of dough into a long roll of about 1-inch diameter. Use two objects with flat edges to shape each roll, such that the long sides of the roll become flat and the side profile is a square.
Place the four rolls in a two-by-two arrangement, such that the cocoa powder doughs are diagonal to one another in a chessboard pattern. Place the dough in the refrigerator for at least 30 minutes.
Remove the dough from the refrigerator and preheat the oven to 350F. Slice off cookies of about ⅓-inch thickness from the dough roll and bake for 10-12 minutes or until the lighter part of the dough becomes lightly golden in color.
Allow the cookies to cool before attempting to transfer them, as they will be delicate while warm.