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Dice the onion. Roughly chop the chestnuts.
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Heat the oil in a large saucepan.
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Fry the onion until transparent.
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Add the chestnuts and sauté.
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Sprinkle with 1 teaspoon of sugar, add pumpkin and sauté briefly.
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Season with salt and pepper.
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Add the vegetable broth.
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Bring to a boil. Lower the heat and let simmer for 25 minutes.
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Puree with a stick blender. Alternately transfer to a blender, puree and return to the pot.
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Stir in the cream.
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Let cook for another 5 minutes.
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Mix in the balsamic vinegar.
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Season again with salt and freshly ground pepper to taste. Add more sugar if needed.
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Transfer to bowls and serve.