In small bowl, whisk together the vinegar, shallot, mustard, salt and pepper. Gradually whisk in oil until thick.
Heat oven to 375 degrees F.
Cut stems from beets, leaving 1 inch of the stems intact. Rub beets with oil. Place in roasting pan.
Bake in 375 degree F oven 75 to 90 minutes or until knife-tender. Remove from oven. When cool enough to handle, trim and peel beets; cut each into 8 wedges. In large bowl, toss with 2 tablespoons vinaigrette.
Bring a small pot of water to a boil. Add the sliced garlic; boil for 1 minute. Drain.
To serve, in large bowl, combine radicchio, arugula and garlic. Add remaining vinaigrette; toss. Arrange beets over greens. Top with cheese. Makes 6 servings.