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.