Clean the mussels with a brush under cold running water and remove the beards.
Melt the butter in a stockpot and sauté the onions until translucent. Add the celery, leek, carrot, salt, peppercorns, bay leaf, parsley and wine. Reduce the heat, cover and simmer for 10 minutes.
Increase heat to high and add the mussels. Cook for 6 to 8 minutes, or until the mussels open. Discard any mussels that remain shut. Strain the broth and serve with the mussels in a large serving bowl. Serve at once with fresh bread.