Knead flour, fat, egg yolk, sugar and vanillin sugar to a short pastry. Chill for at least 1 hour. Grind the almonds. Then mix with sugar, vanillin sugar, cinnamon and milk to a spreadable mixture.
Roll out short pastry between 2 layers of cling film to a square of 25x25 cm. Spread almond paste evenly on top and cut out cookies of approx. 4 cm Ø. Dip the cookie cutters briefly in water to prevent the pastry from sticking to them.
Place the cookies on a baking tray lined with baking paper. Beat the egg white until stiff. Add lemon juice and stir in. 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 cookies. Bake in the preheated oven (electric cooker: 100°C/ gas: level 1) for approx. 50 minutes. Let them cool down on a cake rack.
Store in a cool place in tins. Results in about 30 pieces.