Chilled, cooked mussels in vinaigrette have layers of flavor from Dijon mustard, rice-wine vinegar, olive oil, shallots, and parsley.
Heat 2 tablespoons oil in a large pot over medium heat. Add sliced shallots; cook, stirring, until translucent, about 3 minutes. Add wine; bring to a boil. Add mussels; cover and cook, stirring once, until mussels open, about 3 minutes. (Discard unopened shells.)
Remove mussels with a slotted spoon; discard cooking liquid. Chill mussels in a bowl in the refrigerator, about 1 hour.
Whisk together mustard, chopped shallots, and vinegar; season with salt and pepper. Pour in remaining 1/2 cup plus 1 tablespoon oil in a slow, steady stream, whisking until emulsified. Whisk in parsley. Vinaigrette can be stored in the refrigerator up to 3 days.
Toss chilled mussels with 1/2 cup vinaigrette. If desired, serve on the half shell on a bed of lettuce. Garnish with parsley. Drizzle with more vinaigrette, if desired.