Preheat the oven to 350°F (180°C). Grease and flour a cake pan.
Separate the eggs. In a clean bowl, beat the egg whites with a pinch of salt until stiff peaks form.
In a separate bowl, cream together the egg yolks, granulated sugar, and vanilla sugar until light and fluffy. Add the melted butter and milk, and mix until combined.
Break up the chestnut purée with a fork, and add it to the egg yolk mixture.
In a separate bowl, whisk together the flour, baking powder, and cinnamon.
Gradually add the dry ingredients to the chestnut mixture, mixing until just combined.
Gently fold in the beaten egg whites to ensure the batter remains light and airy.
Pour the batter into the prepared cake pan and spread evenly.
Bake in the preheated oven for approximately 35-40 minutes, or until golden brown and a toothpick inserted into the center comes out clean.
Remove from the oven and let cool completely before dusting with powdered sugar and serving.
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