Preheat oven to 350°F (180°C) and prepare a muffin tin with paper liners.
In a large bowl, whisk together the flour, baking powder, salt, and cinnamon.
In another bowl, mash the bananas with a fork, then add the sugar, eggs, milk, melted butter, and vanilla sugar. Whisk until smooth.
Incorporate the chestnut purée into the banana mixture until fully combined.
Gradually add the wet ingredients to the dry ingredients, gently mixing until just combined. Be careful not to overmix.
Evenly distribute the batter into the muffin liners, filling them about three-quarters full.
Place the muffin tin in the preheated oven and bake for 20-25 minutes, or until the muffins are golden brown and the tops spring back lightly when touched.
Check for doneness with a toothpick: if it comes out clean when inserted into the center of a muffin, they are ready.
Let the muffins cool in the tin for a few minutes, then transfer them to a wire rack to cool completely.
Serve fresh, or store in an airtight container to maintain their softness.
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