Preheat oven to 350°F (180°C). Grease and flour a cake pan.
In a large bowl, whisk together the flour, baking powder, and ground walnuts.
In another bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time.
Stir in the chestnut purée, then gradually add the dry ingredients and milk, mixing until you have a smooth batter.
Pour the batter into the prepared pan and bake for 30-35 minutes, or until a wooden skewer inserted into the center comes out clean. Let cool completely in the pan before frosting.
For the frosting, combine the heavy cream, powdered sugar, and vanilla extract in a bowl. Whip until stiff peaks form.
Layer the cake with the whipped cream frosting, covering the top and sides evenly.
Decorate the top of the cake with chestnut purée, dark chocolate shavings, and ground walnuts.
Refrigerate the cake for at least an hour to allow the flavors to meld. Serve chilled.
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