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1. Heat the olive oil over medium-low heat, add the onion, leek, and celery, and cook gently, stirring often, for about 10 minutes, until very tender. Add 1/2 teaspoon kosher salt after the first 5 minutes. Make sure that the vegetables do not color.
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2. Add the potatoes, garlic, and bouquet garni. Stir together and add the water or stock. Bring to a simmer, add salt to taste, cover and simmer 30 to 40 minutes, until the vegetables are very tender and the broth fragrant. Remove from the heat.
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3. Remove the bouquet garni from the soup. Using an immersion blender, puree the soup (or you can put it through the fine blade of a food mill or use a regular blender, working in batches and placing a kitchen towel over the top to avoid splashing). Then strain through a medium strainer (this step is important; otherwise the soup will be stringy), using a pestle or the bottom of a ladle to push the soup through. Make sure to scrape the outside of the strainer so that all of the puree goes back into the soup. Return to the pot, stir with a whisk to even out the texture, heat through and season well with salt and pepper.
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4. Ladle the soup into bowls and garnish each bowl with a few thin slices of celery and about 1/4 teaspoon walnut oil. Sprinkle with minced chives or chervil if you wish, and serve.
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Advance preparation: You can make this several hours or even a day ahead. Refrigerate in covered containers. When you reheat, whisk the soup to smooth out the puree (it will separate as it sits).
