Preheat oven to 425°.
Leave root and 1 inch of stem on beets; scrub with a brush. Place beets on a small baking sheet coated with cooking spray. Bake at 425° for 1 hour or until tender when pierced with a fork. Cool. Trim off beet roots and stem; rub off skins. Cut each beet in half lengthwise; slice each beet half crosswise into 1/4-inch-thick slices.
Combine leek, oil, and 1/4 teaspoon salt on a baking sheet coated with cooking spray; toss well to coat. Bake at 425° for 15 minutes or until tender and just beginning to brown; stir after 8 minutes.
Combine water, lime juice, peanut butter, ginger, and 1/4 teaspoon salt, stirring well with a whisk until smooth.
Arrange 1/3 cup sprouts on each of 6 salad plates; divide the beets and leek evenly among servings. Drizzle about 2 teaspoons dressing over each serving.