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Heat the oil over high heat in a large Dutch oven with lid. Add in the fennel, carrots, celery, and onion. Cook until they are lightly browned. Add the mussels and sauté for 2 minutes. Water from the mussels will release.
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Add in the tarragon, basil, white wine, court bouillon, and saffron threads. Stir to mix and cover with lid. Reduce heat to medium, and steam the mussels for about 3 to 4 minutes, or until they have all opened.
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Remove the mussels from the pan, and discard any that have not opened.
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Strain the broth and add back to the pan. Bring back to a boil, and whisk in the cream and butter. Let boil for about 2 minutes.
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Arrange mussels on a serving plate and ladle sauce over the top. Serve while hot.