Cut the apricots into thin strips and soak in rum.
Mix the flour with the sugar, vanilla sugar and a pinch of salt, and pile up over the work surface. Make a depression in the center of the flour, add the beaten egg into it and distribute the butter in small pieces around. Quickly knead with your hands to a smooth dough, shape into a ball and wrap in plastic wrap. Let the dough rest for 30 minutes in the refrigerator.
Roll out the dough on a floured work surface to 4 mm thin and cut out round cookies (about 4 cm diameter) (approximately 1½ inches diameter).
Drain the apricots strips well, place over each cookie, fold the cookies into crescents and press the edges firmly. Shape the crescents into rolls and form the crescents again.
Place the crescents on a baking tray lined with baking paper and bake in a preheated oven at 180°C (fan: 160°C, gas mark 2-3) (approximately 350°F) for 8-10 minutes until light golden.
Remove the tray from the oven, pull the baking paper from the tray and roll the cookies in powdered sugar while still warm. Let dry and serve cool.