Line the bottom of the springform w/ baking parchment & grease bottom & edge.
Preheat the oven to 160 degrees C w/ fan.
Grate the lemon zest & press the juice.
Melt the butter & let it cool.
Peel the apples, core them & cut them into thin slices.
Add lemon juice & mix well.
Mix flour & baking powder; add salt & ground rosemary & lemon zest.
W/ a handhelt electric mixer (beater elements) beat the eggs & the sugar until fluffy.
Add flour mix.
Add melted butter.
Fold in the apple slices.
Pour the batter w/ the apple slices - rather thin - into the springform.
Let it bake for about 40 min.
Make the test w/ the wooden pin... maybe add another 5 min.
In the meantime mix water & sugar & bring it to a boil.
Add a sprig rosemary, let it simmer for about 10 min & strain the syrup.
Let the cake in the springform cool down for about 5 min.
Open the springform & remove the edge.
Use the wooden pin to make some holes in the hot cake.
Brush the hot cake w/ the syrup which is absorbed by the the cake immediately.
Finally sprinkle the vanilla sugar on top.
When at room temperature shift the cake on a cake platter & remove the baking parchment.