Knead flour, fat, sugar, vanillin sugar and egg to a smooth short pastry. Wrap in foil and chill for about 1 hour. Roll out the dough thinly on a floured work surface and cut out 40 round cookies (approx. each 4-4.5 cm Ø).
Cut out 40 moons from the remaining dough. Place on baking trays lined with baking paper and bake in the preheated oven (electric oven: 200°C/ gas: level 3) for about 10 minutes one after the other.
Let it cool down on a cake rack. Melt the couverture separately on a hot water bath. First coat the moons with white couverture. Then place the round cookies with the dark couverture and the moons immediately on top.
Allow to dry. Results in about 40 pieces.