Preheat the oven to 160° C fan.
Oil the springform.
Grate the lemon zest, press out the lemon juice & set aside.
Mix butter, sugar, vanilla sugar & salt w/ the handheld electric mixer until creamy & well combined.
Add eggs & mix.
Add flour, baking powder & lemon zest & mix.
Add milk & mix.
When all is well combined finally add the lemon juice.
Pour the cake batter in the prepared springform & put it in the oven for about 35 - 40 min.
Make the well-known test w/ the wooden skewer ... & decide if it's necessary to add another 5 min in the oven.
Let the cake cool down for about 10 min - then remove the edge of the springform.
Let it cool to room temperature & transfer the cake to its final plate.
Grate the lemon zest for the icing & press out the lemon juice.
Whisk together icing sugar, lemon zest & lemon juice - save some lemon zest for final decoration.
Spoon the icing over the cake - be aware that it will run down the egde ... more or less ...
Sprinkle the lemon zest over the cake.
Put the cake in the fridge to let the icing set a little.