Mix the softened butter with sugar and vanilla sugar until frothy. Add the eggs one at a time. Mix the flour with baking powder and stir in together with the lemon zest.
Spread the dough on a greased or lined baking sheet and bake in a preheated oven at 175-200 degrees for 20-30 minutes.
For the topping, sieve the powdered sugar and place in a bowl, stir with lemon juice to a topping and glaze the cake with it.