Place the puff pastry slices next to each other on a floured work surface and let them thaw for about 10 minutes. In the meantime, separate 2 eggs. Put the egg white and 1 egg yolk aside separately. Mix marzipan, icing sugar, remaining whole eggs and egg yolks, rum, ground and chopped almonds to a smooth mixture.
Beat the egg white until stiff and fold into the marzipan mixture. Moisten the puff pastry sheets with water, place them on top of each other and roll out into a square (40x40 cm). Spread the marzipan mixture evenly on top and roll everything up.
Place the roll on a baking tray lined with baking paper and let it rest in the refrigerator for 15-20 minutes. Whisk aside the egg yolk with 1 teaspoon of water, brush the roll with it and sprinkle with sugar crystals.
Bake in the preheated oven (electric oven: 200 °C/ gas: level 3) for about 45 minutes. Results in about 20 slices.