In a small bowl, mix mustard with 4 teaspoons water until smooth; let stand 5 minutes. Whisk in lemon juice, honey, miso, oil, and ginger.
Trim and discard tops and root ends from beets. Scrub beets well, then pare peel with a vegetable peeler and discard. Using the vegetable peeler or a mandoline, slice beets paper thin. Arrange slices equally, slightly overlapping, in a ring on each of four salad plates.
In a bowl, mix 2 tablespoons ginger-miso vinaigrette with salad mix. Arrange greens equally in the center of beets. Drizzle remaining dressing over beets. Add salt and pepper to taste.