Discard any mussels that have cracked or are damaged. Remove beards from mussels, and scrub each mussel under cold water. Rinse until water runs clear.

Combine the wine, shallots, bay leaf, and thyme in a very large pot and bring to a slow simmer over medium heat.

Add the mussels to pot, and turn heat up to high. When steam starts to escape from cover, reduce heat to medium. Shake pot to redistribute mussels, and cook for 5 to 10 minutes, or until mussels have opened. Remove from heat, remove mussels from liquid and discard any unopened mussels.

Pass the broth through a fine sieve into another saucepan. Reduce liquid on high heat for 2 minutes. Remove from heat, and with a hand held blender add the olive oil, Dijon, and tarragon. Season with salt and pepper and spoon over mussels.