Beat the butter, sugar and eggs until frothy. Add the vanilla sugar, salt and rum. Mix the flour and baking powder and stir into the batter. Peel and core the apples, cut into small pieces and stir into the batter as well. Grease a springform pan (diameter 26 cm) and pour the dough into it. Bake at 200 degrees or gas mark 3 for about 20 minutes.
Now carefully heat the remaining 20 g butter so that it becomes liquid. Beat together with the eggs and sugar until frothy and pour over the hot cake. Bake for another 20 minutes until golden brown. Let the cake cool in the pan.