For the chestnut slice, first prepare the sponge dough. To do this, preheat the oven to hot air at 180°C. Line two baking trays with baking paper. Separate the eggs and beat the beaten egg whites with the sugar until stiff. Gradually add the egg yolks. Finally, fold in the flour. Spread the mixture on the two trays and bake in the oven for about 15 minutes (be careful to swap the positions of the trays once).
For the cream, beat the butter until fluffy, add the sugar. Add the chestnut rice and season with rum.
Let the sponge cool and remove it from the baking paper. Put one side back on a baking sheet. Spread the cream evenly on it. Place the second part of the sponge on top and cut off the sides all around so that the chocolate can run over it. Spread the melted chocolate over it and refrigerate the chestnut slice.