In a large saucepan combine the onion, bay leaf, garlic, carrot, fish stock and wine. Bring to a boil and cook for about 5 minutes to soften the carrot and onion.
Add the mussels to the boiling mixture, cover and cook over high heat until the mussels open, about 5 minutes. Shake the pan occasionally to help them cook evenly.
As soon as the mussels have opened remove them with a slotted spoon and set aside. Remove the bay leaf from the broth and stir in the heavy cream. Heat through, but do not boil. Taste and season with salt and pepper. Salt may not be necessary depending on the saltiness of your fish stock.
Place mussels into serving dishes and spoon broth over them.