1. Preheat oven to 400°. Peel sweet potatoes, and cut into 3/4-inch cubes. Peel parsnips, and cut into 1/2-inch slices. Peel beets, and cut into 1/2-inch-thick wedges.
2. Toss sweet potatoes and parsnips with 2 Tbsp. olive oil in a large bowl; place in a single layer in a lightly greased 15- x 10-inch jelly-roll pan. Sprinkle with 1 1/4 tsp. salt and 1/2 tsp. pepper.
3. Toss beets with remaining 1 Tbsp. olive oil; arrange beets in a single layer on a separate aluminum foil-lined 15- x 10-inch jelly-roll pan. Sprinkle with remaining 1/2 tsp. salt and 1/2 tsp. pepper.
4. Bake at 400° for 40 to 45 minutes or just until tender. Let cool completely (about 20 minutes).
5. Meanwhile, whisk together dressing and next 3 ingredients. Place vegetables in a large bowl, and drizzle with desired amount of dressing; toss gently to coat. Serve at room temperature or chilled over arugula with any remaining dressing.