Scrub the mussels under cold running water, removing any barnacles by knocking off with the back of a knife. The beards that hang from between the closed shells can be tugged off sharply by hand.
Melt the butter in a heavy based, large saucepan and add the shallots and garlic, saute slightly until beginning to soften. Add the mussels and stir well. Immediately add the white white and chopped parsley. Season with a few grinds of pepper. Stir again.
Place the lid on the saucepan and leave the mussels to steam open, giving the pan a shake from time to time. They will take about 3 or 4 minutes until all are fully opened. Any that don't open should be discarded.
Stir in the double cream, taste and correct the seasoning. Ladle into bowls and garnish with more chopped parsley.