In a large bowl, whisk together the flour, baking powder, cinnamon, and vanilla sugar.
In a separate bowl, cream together the butter and sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition.
Mash the chestnut purée with a fork, then mix in the milk until smooth.
Add the chestnut mixture to the butter-egg mixture and combine until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Pour the batter into a greased and floured Bundt pan, spreading it evenly.
Bake in a preheated oven at 350°F (180°C) for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Let the Bundt cake cool in the pan for 10 minutes, then carefully invert it onto a wire rack to cool completely.
Dust with powdered sugar or sprinkle with cinnamon sugar before serving.
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