For the apple cinnamon pie, chop the peeled apples and mix with apple juice, lemon juice and cinnamon. Cover and steam until soft, about 5 to 8 minutes, then puree. Then soak the gelatine in cold water and dissolve in the applesauce, add sugar and vanilla sugar. Add rum and let the mixture cool.
For the sponge cake, beat the egg whites with 40 g sugar until stiff, separately beat the 3 yolks with 40 g sugar until foamy. Sift the flour with the cornflour and carefully fold both into the yolk mixture, alternating with the egg mixture. Finally, stir in the butter. Spread on a prepared baking sheet and bake at 220°C for 8-10 minutes until light. Cut out a sponge sheet, stir the yogurt into the cooled, not yet set apple mixture and finally fold in the whipped cream, which should not be too stiff.
Place the sponge sheet in a high cake tin, spread with currant jam and fill with the yogurt-apple mixture. Place sponge cake on top of the apple cinnamon cake and press down lightly. Chill for about 4 hours and allow to set. Sprinkle with cinnamon if desired.