Combine the chestnut puree, butter, and sugar in a bowl and mix until smooth and creamy.
Add the eggs one at a time to the chestnut mixture, mixing well after each addition.
Sift together the flour, baking powder, and cocoa powder, then gradually add to the wet ingredients, mixing until just combined.
Stir in the rum extract for an intense, spiced flavour.
Pour the batter into a greased and floured cake pan, spreading evenly. Bake in a preheated oven at 350°F (180°C) for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
While the cake cools, prepare the cream: whip the heavy cream to stiff peaks and melt the dark chocolate over a double boiler.
Fold the whipped cream into the melted chocolate until you have a rich and creamy frosting.
Frost the cooled cake with the chocolate whipped cream and sprinkle with cocoa powder. If desired, garnish with chestnut pieces or chocolate shavings.
Refrigerate the cake for at least 2 hours to allow the flavors to meld and the frosting to set.
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