Preheat the oven (350 °F/180 °C). For the dough, beat the butter with the sugar and vanilla sugar using the whisk attachments on the hand mixer. Add the eggs one at a time. Mix the flour, baking powder and salt together and sift onto the butter and egg mixture. Add the milk and mix everything together to form a smooth dough.
Grease the loaf tin with butter and dust with flour. Pour in the dough and bake on the middle shelf of the oven for approx. 45 minutes. Then allow to cool a bit, turn out of the tin and leave to cool completely on a cooling rack.
For the lemon icing, mix the icing sugar and lemon juice to a creamy consistency and spread over the cake. Sprinkle with pistachio nuts, allow the icing to set and serve. Enjoy!