Heat the olive oil in a large saucepan until shimmering. Add the onion and garlic and cook over moderately high heat, stirring occasionally, until softened, about 6 minutes. Add the turnips and cook, stirring frequently, until crisp-tender, about 5 minutes. Add the wine and cook until almost evaporated, about 5 minutes. Add the 4 cups of chicken stock and bring to a boil. Reduce the heat to moderately low and simmer until the turnips are tender, about 25 minutes.
Working in batches, puree the soup in a blender or food processor, then strain it through a fine sieve. Return the soup to a clean saucepan, stir in the scallions and cook over moderate heat for 5 minutes. Whisk in the crème fraîche until fully incorporated; thin the soup with stock if necessary. Season with salt and pepper.
Ladle the soup into shallow bowls and serve with the Cheese Crisps.
The soup can be refrigerated overnight. Gently reheat.
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