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If using vacuum packed chestnuts, follow the package directions for cooking in boiling water then opening. If using raw chestnuts, place in a large pot of cold water and bring to a boil. Simmer for three minutes. Remove a few at a time with a slotted spoon, keeping the rest in the water so that their skins stay soft enough to score open. Using a sharp paring knife, peel the chestnuts and set aside until ready to use.
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Heat 2 tablespoons of butter and 2 tablespoons olive oil over medium heat in a large soup pot and cook the fennel, leeks, and garlic until soft and glistening, about 10 minutes, stirring. Add the potatoes and 50 cleaned chestnuts and stir to coat in the oil.
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Pour in the ouzo. As soon as the alcohol steams off, add the chicken or vegetable stock. Bring the soup to a simmer and cook, covered, for about 40 minutes. Using an immersion blender purée the soup in the pot, or transfer the soup in batches to the bowl of a food processor and puree until smooth. Although it isn’t necessary, you can strain the soup through a fine-mesh sieve or chinois for a silkier texture and more elegant result. Taste and adjust seasoning with salt and pepper.
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Bring the soup back to a simmer, add the cream and stir. Adjust seasoning. Right before serving, stir in the remaining butter. Serve in individual bowls with a dollop of Greek yogurt, one chive or fennel sprig, a drizzling of extra-virgin olive oil and crushed pink peppercorns.