Prepare the ingredients. Melt the butter and, if necessary, break up the chestnut purée with a fork to make it smoother.
In a bowl, whisk the eggs with the granulated sugar and vanilla sugar until light and fluffy.
Add the melted butter and milk to the egg mixture and mix well to combine.
In a separate bowl, whisk together the flour, rolled oats, baking powder, and a pinch of salt.
Gradually add the dry ingredients to the wet ingredients, mixing thoroughly until you have a smooth batter.
Add the chestnut purée and gently fold it into the batter until just combined. The batter will be quite thick, but don't worry, that's the correct consistency.
Grease and flour a Bundt pan. Pour the batter into the prepared pan and bake in a preheated oven at 350°F (180°C) for 40-45 minutes.
Once the Bundt cake is baked, test for doneness by inserting a toothpick into the center. If the toothpick comes out clean, the cake is ready.
Let the cake cool completely before slicing and serving. If desired, dust with powdered sugar before serving.
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