Trim fennel stalks flush with bulbs and discard stalks. Quarter bulbs lengthwise and cut out most of cores, leaving enough to keep pieces intact. Cut quarters lengthwise into thin slices.
Toast mustard seeds in a dry small heavy skillet over moderate heat, stirring constantly, until mustard seeds begin to pop and turn 1 shade darker, about 3 minutes. Transfer to a plate to cool.
Whisk together vinegar, Dijon mustard, and salt and pepper, to taste, then add oil in a slow stream, whisking until emulsified. Stir in shallot and mustard seeds.
Toss together fennel, romaine, frisee, endives, and parsley in a large bowl. Serve with dressing on side.
Fennel may be trimmed and sliced 1 day ahead and chilled in a sealable plastic bag lined with dampened paper towels.
Dressing may be made 2 days ahead and chilled, covered. Bring to room temperature and season before serving.