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Wash the mussels and pull off any beards that may still be attached to the shell. A pair of needle-nose pliers works well for this. Discard any mussels with cracked or broken shells and those that do not remain closed.
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In a large Dutch oven or a stainless steel wok with a lid, melt the butter over medium heat and add the garlic and shallots. Lightly season with salt and pepper. Sauté for a minute or two, just enough to soften the shallots a little.
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Add the wine and boil for about 3 minutes or so to reduce the volume of the liquid by about 1/3.
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Add the mussels to the pot and cover immediately. Shake the pan occasionally and steam the mussels for only 3 minutes.
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Remove the mussels to a plate but keep the liquid in the pot. Add the lemon juice, lemon zest, whipping cream and Dijon mustard. Stir until well blended. Taste the liquid and add a final seasoning of salt and pepper if needed. The salt from the mussels usually seasons the liquid sufficiently.
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Add the mussels back to the pan, sprinkle on the tomatoes and then put the lid back on the pot. Steam for an additional minute or 2 to reheat the mussels only.
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Remove the mussels to large serving bowls and pour the liquid from the pot all over them.
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Serve with toasted, buttered pieces of baguette to dunk in the sauce.