Preheat the oven to 350°F (180°C) and line a cake pan with parchment paper.
In a large bowl, separate the eggs. In another bowl, whisk the egg yolks with the sugar and vanilla sugar until pale and fluffy.
Add the flour, baking powder, and a pinch of salt to the egg yolk mixture. Mix until just combined.
In a clean bowl, whisk the egg whites until stiff peaks form. Gently fold the egg whites into the batter.
Pour the batter into the prepared cake pan and bake for 25-30 minutes, or until golden brown and a toothpick inserted into the center comes out clean. Let cool completely in the pan.
Mix the chestnut puree with the rum extract. Whip the heavy cream until stiff peaks form. Gently fold the whipped cream into the chestnut mixture.
Slice the sponge cake into two or three layers. Spread the chestnut cream evenly between each layer.
Melt the dark chocolate and drizzle it over the top of the cake for decoration.
Refrigerate the cake for at least 2 hours to allow the flavors to meld.
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