Cut cabbage into thin shreds and chop parsley. In a small bowl whisk together mustard, vinegar, and salt until combined.
Whisk in oil in a slow stream, whisking until emulsified.
In a large bowl toss together cabbage, parsley, vinaigrette, and salt and pepper to taste until combined. Chill salad, covered, at least 30 minutes and up to 2 hours.