Preheat the oven to 350F. In the bowl of an electric mixer, cream together the butter, sugar, and vanilla sugar until light and fluffy.
Add the all-purpose flour, cake flour, baking powder, and cocoa powder and mix until just combined.
Separate the dough into four pieces. Roll each piece to about 1 inch in width. Place two of the rolls on a baking sheet, parallel to the length of the baking sheet. Lightly flatten each roll with your hands. Repeat with the remaining two rolls on a second baking sheet.
Crack the egg into a medium-sized bowl and whisk the egg until the yolk and white are combined. Lightly brush a small amount of the egg wash along the length of each roll. Sprinkle pearl sugar on top.
Bake for 10-12 minutes or until the cookies become slightly firm, rather than completely gooey or chewy.
After removing the cookies from the oven, and while they are still hot, slice the rolls diagonally to make the cookie cuts.