Cream fat, sugar, vanilla sugar, rum, egg and salt with the whisk of the hand mixer. Sieve the flour and baking powder into a bowl, make a depression in the middle and add the fat-sugar mixture and milk and knead to a smooth dough.
Heat the oil in a pot (approx. 180 °C). Roll out the dough on a well floured work surface to a thickness of 3-4 mm, cut out drops with a drop cutter (7 cm long, 3.5 cm wide, at the widest point).
Put 6-8 capfuls each into the hot oil and fry them until golden brown. After half of the frying time turn the caps with a skimmer. Lift the capes out of the frying fat with a skimmer, let them drip off on kitchen paper and dust the warm pastry with icing sugar.
Do the same with the remaining dough.