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Melt 3 tablespoons of butter in a heavy pot. Add in the shallot and cook over medium heat until softened. Add in the mussels, white wine, fennel bulb, and the court bouillon.
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Cover, and bring to a boil. Steam the mussels, shaking the pan occasionally to stir them up, for about 5 to 7 minutes, or until the mussels steam open. Remove mussels with a slotted spoon, and remove the meat from the shells. Reserve.
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Strain the liquid, pressing on the solids to extract any left over liquid, and bring it to a boil. Reduce until there is about a cup of liquid. Add in the cream, and boil gently until the sauce coats the back of a wooden spoon. Whisk in the remaining butter pats.
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Add back the mussel meat, and season with salt and pepper. Just before serving, stir in the chopped chives and fennel tops.
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Serve immediately.