Preheat your oven to 350°F (180°C). Grease and lightly flour a Bundt pan to prevent the cake from sticking.
In a large mixing bowl, whisk together the flour, baking powder, ground cinnamon, and vanilla sugar.
In another bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs one at a time to the butter mixture, mixing well after each addition to ensure the batter remains light and airy.
Mash the bananas with a fork, then stir in the chestnut puree until well combined.
Alternately add the dry ingredients and milk to the butter mixture, then stir in the banana-chestnut mixture until just combined. Do not overmix.
Pour the batter into the prepared Bundt pan and spread evenly using a spatula.
Bake in the preheated oven for approximately 40-45 minutes, or until a toothpick inserted into the center comes out clean. Avoid opening the oven during the first 30 minutes, as this may cause the cake to collapse.
Once baked, let the cake cool in the pan for 10 minutes before inverting it onto a wire rack to cool completely.
Before serving, dust with powdered sugar and slice. It's delicious with a cup of hot tea or coffee.
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