Place flour, fat, egg yolk, sugar and vanilla sugar in a mixing bowl and work through with the dough hooks of the hand mixer. With cool hands quickly knead to a smooth dough.
Wrap in foil, cover and chill for about 1 hour. Mix nuts, sugar, vanillin sugar, cinnamon and milk to a spreadable mixture. Roll out short pastry between two layers of cling film to a rectangle of 25 x 18 cm.
Spread the hazelnut mixture evenly on the dough. Use a damp knife to cut sticks 5 cm long and 2 cm wide. Spread on two baking trays lined with baking paper. Beat the egg white until stiff.
Stir in lemon juice. Sift icing sugar over it. Add rum and carefully fold both into the beaten egg white. Pour into a piping bag with a perforated spout and squirt onto the hazelnut sticks. Bake both trays in the preheated oven (electric oven: 125°C/ gas: level 1) one after the other for about 50 minutes.
Let it cool down. Pour into tins and store in a cool place. Results in about 45 pieces.