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Leek: Cut off and discard the top of the leek, where it becomes light green.
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Cut in half and rinse until all dirt is gone.
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Thinly slice the leek into ¼’ pieces.
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Fennel: Cut the bulb in half and cut out the center. Slice into ¼ inch pieces.
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Heat the olive oil in a medium pot over medium heat. Add the leek and cook for 8 minutes until softened and translucent, but not browned.
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Add the fennel, stock, tomatoes, and salt (omit if using canned or boxed).
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Bring the soup to a boil; reduce heat to low and cook until fennel is soft, very important. About 30 minutes.
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Add the tarragon.
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Transfer soup to a food processor in small batches and blend until pureed.
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Return to the pot and taste for salt and pepper. Reheat and serve.