Beat butter with powdered sugar until fluffy. Gradually stir in the flour.
Halve the dough (try to be exact – you may want to use a kitchen scale).
Mix the nuts and cocoa into one half of the dough, and mix the cornstarch and vanilla extract into the other.
Roll out the dough for the different patterns (see below) and chill in the fridge overnight (or for at least a couple of hours).
Checkerboard pattern: Roll out (approx. 1/2 inch thick), cut both dough varieties into equal strips and layer them, then gently press together. Or, you can put the rolled dough pieces directly on top of each other and cut both at the same time.
Swirly snail pattern: Roll out (approx. 1/4 inch thick), put the dough types on top of each other, and roll up firmly, then slice.
After chilling, cut the cookies into checkerboard squares or swirly slices and bake for about 10-15 minutes at 180°C/350°F.