In a small bowl whisk together vinegar, shallot, honey, mustard, and salt and pepper to taste. Add oil in a slow stream, whisking until emulsified. Vinaigrette may be made 1 week ahead and chilled, covered. Bring vinaigrette to room temperature before using.
Trim radicchio and tear into bite-size pieces. In a large bowl toss together radicchio, baby greens, and parsley.
Just before serving, drizzle vinaigrette over salad and toss well with salt and pepper to taste.