Remove beards on mussels, and scrub shells well with a brush. Discard opened or cracked mussels, or any heavy ones (they're filled with sand).

Bring wine to a boil in a large Dutch oven. Add mussels; cover and simmer 8 to 10 minutes or until shells open, shaking pot several times. When shells open, transfer to a bowl, reserving liquid in pan. Let mussels cool slightly. Discard halves of shells to which mussels are not attached. Loosen mussels remaining in shells, and arrange shells, open side up, on serving plates.

Strain reserved cooking liquid into a large skillet. Add green onions, parsley, lemon juice, and pepper. Cook over high heat until liquid is reduced to about 1/2 cup. Remove from heat, and whisk in butter until butter melts and sauce is thick. Spoon sauce over mussels, and serve immediately with French bread, if desired.