Heat the butter in a large saucepan until melted. Add the onions, shallots and garlic, and cook briefly, until wilted. Do not brown.
Add the mussels, salt, pepper, bay leaf, thyme, white wine, and cream. Cover closely and bring to a boil. Cook for about 5 minutes, shaking to redistribute the mussels. Cook until all the mussels are opened.
Using a slotted spoon, transfer the mussels to a serving bowl. Keep warm. Continue cooking the sauce for a minute, remove bay leaf and the thyme. Stir in the mustard with a wire whisk while heating. Do not boil.
Season sauce to taste with salt if necessary, then spoon equal portions of it over the mussels, and sprinkle with parsley. Serve immediately with crusty bread.