Preheat oven to 400 degrees F (200 degrees C). Grease a rimmed baking sheet with 1 tablespoon butter.
Combine 1 1/2 cups butter, sugar, and vanilla sugar in a large bowl; beat with an electric mixer until smooth and creamy. Add eggs one at a time and beat after each addition until well combined. Mix in flour and baking powder on low speed until well combined; mix in lemon zest.
Spread dough on the prepared baking sheet. Use a spatula as dough is very sticky.
Bake in the preheated oven until set, about 20 minutes. Let cool completely, about 30 minutes.
Mix confectioner's sugar and lemon juice in a small bowl and brush glaze onto the cooled cake. Allow to dry, about 15 minutes.