Melt the butter in a nonreactive saucepan. Add the celery, shallots, garlic and thyme and cook over moderate heat, stirring, until the vegetables soften. Add the beer and parsley and bring to a boil over high heat. Add the mussels, cover and steam, shaking the pan, until they open, about 5 minutes. Scoop the mussels into bowls, discarding any that don't open. Season the broth with salt and pepper and pour over the mussels.