Separate eggs. Beat the egg whites until stiff, pour in the sugar. Fold in egg yolks. Mix flour and baking powder, sieve over it and fold in. Spread the mixture on a baking tray covered with baking paper.
Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for approx. 10 minutes. Take out and turn onto a damp tea towel. Carefully peel off the paper and roll up the sponge cake from the long side in the tea towel.
Let it cool down.
Clean the pineapple (put a few leaves aside for decoration), peel and cut or slice very thinly. Heat butter in a large pan. Steam pineapple slices in it at low heat for 2-3 minutes.
Put it on a plate.
Mix jam and 1 tablespoon of rum in a pot, bring to the boil once and puree. Mix 2 tablespoons rum and syrup. Roll out the sponge cake and spread with first syrup, then 3/4 jam. Roll up the sponge cake.
Sponge roll with rest of jam and cover with pineapple slices. Decorate roll with pineapple leaves and candied pieces. Dust with some icing sugar.