How to Make It
Using kitchen string, tie the parsley and thyme sprigs with the bay leaf to make a bouquet garni. Melt the butter in a large enameled cast-iron casserole. Add the bouquet garni, shallots, leek, celery, carrot, garlic, 1/2 teaspoon each of salt and pepper and the cayenne. Cook over moderate heat, stirring occasionally, until the vegetables are softened, 6 to 8 minutes. Add the wine and boil until reduced by half, 4 to 5 minutes. Add the mussels, cover and cook, shaking the casserole occasionally, until the mussels are wide open, 4 to 6 minutes.
Using a slotted spoon, transfer the mussels and vegetables to a large bowl; discard the bouquet garni. Remove the mussels from their shells and add them to the vegetables. Strain the mussel broth through several layers of cheesecloth. Rinse out the casserole.
Return the broth to the casserole. Stir in the cream and bring to a simmer over moderate heat. In a medium bowl, gradually whisk 1/4 cup of the creamy broth into the egg yolks. Whisk the yolk mixture into the simmering soup and immediately remove the pot from the heat. Stir in the mussel and vegetable mixture and the chives and season with salt and pepper. Serve the soup with crusty bread.