Sift flour into a bowl and mix in the sugar, vanilla sugar and baking powder. Form a hollow in the centre and pour in the eggs.
Add the butter and work into a smooth dough. Wrap dough in cling wrap and chill for 1 hour.
Preheat oven to 180 C.
Shape dough into a long roll. Cut into 1cm thick slices and shape each piece into a pencil-thin roll. Shape into small pretzels and place on a greased baking tray. Bake for 18-20 minutes in preheated oven. Allow to cool.
Icing: Stir icing sugar with rum and brush pretzels with it.