Clean, wash and drain the mussels. Clean, peel, wash and cut carrots and celery into thin strips. Leek clean, wash and cut into rings of about 1 cm width. Wash parsley and shake dry.
Pluck off leaves and chop finely. Peel and halve the onion and cut into thin strips.
Heat the fat in a large pot or frying pan and sauté the vegetables and bay leaf until the onions are translucent. Add mussels and steam for about 3 minutes, deglaze with wine.
Cover the mussels and simmer for about 5 minutes until almost all the mussels are open. Stir from time to time. Add cream and parsley to the pot, except for some garnish. Bring to the boil and season the stock with salt, pepper and sugar.
Arrange mussels.