Wash the currants, pluck them from the panicles and drain well. Dice the marzipan and place in a mixing cup. Add the egg and whisk smooth with the whisk of the hand mixer. Roll out the dough on the baking paper on a work surface.
Spread the marzipan mixture thinly. Spread the currants evenly on top, leaving 1 cm of edge free all around. Roll up the dough from the long side using the baking paper. Cut the dough into approx. 15 slices with a floured knife (always clean it from time to time).
With the cut surface facing downwards, carefully place on two baking trays lined with baking paper. Bake one after the other in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for about 15 minutes.
Put it on a cake rack. Stir icing sugar and 2-3 tablespoons of water until smooth. Brush the still warm snails with the icing. Best served lukewarm.