Heat 1 tablespoon of the olive oil and the butter in a saucepan over a medium-low heat and sweat the onion for about 10 minutes, until soft and translucent. Add the sage and garlic and sauté for a minute.
Pour in the stock and add most of the chestnuts – reserve a handful for finishing. Season with salt and pepper, increase the heat and simmer for 15 minutes, stirring from time to time.
Remove from the heat and cool slightly, then purée until very smooth in a blender or food processor, or using a stick blender. Return the soup to the pan, add the crème fraîche and adjust the seasoning if necessary. Warm through gently – do not let it boil.
Meanwhile, slice the reserved chestnuts. Heat the rest of the olive oil in a small frying pan over a medium heat and sauté the sage leaves for a few seconds until crisp, then drain on kitchen paper.
Ladle the soup into warmed bowls, scatter on the chestnuts and sage leaves and add a trickle of olive oil. Finish with a generous grinding of black pepper. Serve immediately.
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