Brush the mussels under cold running water. They are usually sold cleaned. However, if there are still barnacles on the shell, scrape them off with a small knife.
Now sort the mussels for the first time: Closed mussels can be further processed. Once they are open, tap against the shell or the mussel on a surface. When it closes, continue processing.
Keep it open, be sure to sort it out and throw it away!
At the same time, if present, grasp the beard - these are the adhesive threads with which the mussel clings to rocks etc. - with a knife blade and thumb and pluck off.
Onions peel, halve and in strips cut. Clean or peel and wash the soup greens. Cut leek into rings, carrots and celery into thin sticks. Heat butter in a very large pot.
Brown the onions and vegetables.
Add the mussels and bay leaf, pour on the wine. Put the lid on and bring to the boil over high heat. Then cook over medium heat for about 8 minutes. Shake the pot vigorously from time to time to allow the mussels to mix and open more easily.
In the meantime wash parsley, shake dry, pluck off leaves and chop finely.
Remove mussels and vegetables with a skimmer. Now sort a second time: throw away any mussels that haven't opened. Add cream to the stock, simmer briefly and season to taste with salt, pepper and 1 pinch of sugar.
Pour over the mussels, sprinkle with parsley. Serve with baguette.