Scrub mussels. Pull off beards, the tuft of fibers that attach each mussel to it's shell, cutting them at the base with a paring knife. Discard those that do not close when you handle them and any with broken shells. Set aside.

Combine onion, garlic, 4 tablespoons parsley, bay leaf, thyme, wine, and 2 tablespoons butter in large pot. Bring to boil. Lower heat, and cook 2 minutes. Add mussels, and cover. Cook just until shells open, 3 to 4 minutes. Do not overcook. Remove mussels from sauce, and place in bowls.

Strain liquid, and return to pot. Add remaining butter and parsley. Heat until butter melts. Pour over mussels.