1. Preheat oven to 400°.
2. Trim roots and stems from beets. Pierce beets with a fork, and wrap in foil. Bake at 400° for 1 hour or until tender. Cool; peel beets and cut into 1/4-inch-thick slices.
3. Combine chives and next 6 ingredients (through mustard) in a small bowl, stirring with a whisk. Combine cherry tomatoes and about 5 teaspoons mustard mixture; toss to coat. Divide sliced beets and sliced tomatoes evenly among 6 plates. Drizzle each serving with about 3 teaspoons remaining mustard mixture. Top each serving evenly with cherry tomatoes. Sprinkle with salt and pepper.