Beat powdered sugar and room temperature butter with a mixer until light and creamy. Add vanilla sugar.
Add sifted flour to the butter, mix gently with a spatula or at low speed of the mixer.
Add chocolate to the dough and stir it with a spatula.
Divide the dough in half, roll each part into a sausage, wrap in cling film and refrigerate for 1 hour.
Line baking trays with baking paper and preheat oven to 180 degrees.
Cut the dough into circles up to 8 mm thick, place on baking sheets. Bake the cookies for 7 minutes on one side, then 5-8 minutes on the other side. The cookies should harden slightly, but remain light.
Cool the cookies on the baking sheet, transfer to a plate.
Melt the chocolate for decoration in a water bath. Dip one side of the cooled cookies into the melted chocolate and place them on a wire rack until the chocolate has completely hardened.