Preheat the oven to 200°C (approximately 400°F) (fan oven 180 ° C, gas mark 3-4). Beat the butter together with sugar, vanilla sugar and salt until fluffy. Add the eggs one at a time until fully combined.
Mix the flour with the baking powder, sift over the top and stir in. Dissolve the baking soda in the milk, pour in and stir to combine to form a smooth, relatively stiff dough.
Line a baking sheet with parchment paper. Distribute 2 tablespoons of dough, leaving adequate distance between each on the parchment paper. Bake in the oven on the middle rack until golden brown, about 15-20 minutes. Remove and let cool.
Stir the powdered sugar with lemon juice and coat the flat side of the cookies. Allow to dry, then serve.