Dough: Preheat the oven to 180 degrees C. Grease a springform tin.
Whisk the egg yolks and the sprinkle the sugar in. Whisk the egg whites until stiff then sprinkle the vanilla sugar in. Fold the egg whites into the egg yolks.
Sieve the flour with the baking powder into a bowl and fold into the eggs.
Pour the dough into the prepared springform tin and bake in the preheated oven for about 25 minutes.
Cream: Stir sugar, butter and egg yolks until fluffy. Prepare gelatine according to instructions and heat. Add the rum to the gelatine then mix. Add to the fluffy mixture. Fold in the whipping cream.
Rinse a glass bowl with a diameter of about 26-28cm with cold water.
Pour in 1/3 of the cream, cover with the sponge fingers, add another layer of cream and continue making alternate layers until all the cream and boudoir fingers have been used up. Put the bowl into the fridge for about 12 hours.