Scrub the mussels, discarding any that do not close when tapped hard on the side of the sink or that are broken or feel very heavy (they will probably contain sand).
Get out a large pan with a lid and melt the butter in it, add the chopped shallot and the celery, and let it cook over a moderate heat until it is soft but uncoloured.
Pour in the wine and bring it up to the boil. Tip in the mussels and let them cook for about 3 minutes, shaking the pan from time to time.
Lift the lid, check that the mussels are open wide (and if not, then let them steam a little longer), then throw in the chopped parsley and grind over some pepper. Discard any mussels that have not opened.
Pile the mussels into a warm dish, then pour the liquor over them, taking care to leave any gritty bits in the bottom of the pan.