In a large stockpot, melt butter over medium-high heat. Add one shallot and cook, stirring occasionally, until translucent, about 3 minutes. Add mussels and wine. Cover, and cook until all the mussels are open, about 5 minutes. Using a slotted spoon, remove the mussels from the broth, and let cool. Discard any unopened shells. The mussels can be made ahead up to this point and refrigerated for up to 1 day.
In a large bowl, whisk vinegar, remaining 2 shallots, and mustard to combine. Season with salt and pepper. Slowly whisk in olive oil. Add parsley, and whisk to combine. Add mussels; toss with two large spoons to combine. Serve immediately.