Arrange equal portions of the roasted beet slices in one layer on four salad plates. Drizzle a scant 1 teaspoon of the vinaigrette over the beets. Sprinkle the goat cheese over each plate of beets. Sprinkle all but 1 tablespoon of the walnuts over each of the four plates as well. In a small mixing bowl, combine the frisee, watercress, and radicchio. Drizzle 2 tablespoons of the vinaigrette over the greens and toss lightly. (Taste a piece of lettuce; if you want more dressing, toss just a small amount more with the greens, but don't overdress.) Lift a quarter of the greens and arrange them in a tall mound centered on top of the beets (some of the beets should be peeking out underneath) on one plate; repeat with the remaining greens. Sprinkle the remaining walnuts over each salad and serve right away.

Heat the oven to 450 degrees F. Cover two large rimmed baking sheets with parchment. Slice off the tops and bottoms of the beets and then slice the beets into rounds as thin as possible (1/8-inch thick is ideal). If your beets are large and tough, cut them in half first, lay them on their sides, and cut half moons instead of rounds for safer cutting. Toss the slices well with the olive oil, salt, and thyme and spread them in one layer, with a little space between each, on the two baking sheets. Roast for 20 to 25 minutes, swapping the pans to opposite racks halfway through. The beets will be soft and shrunken, slightly glistening on top and dark around the edges. The thinnest slices will be crisp and almost burned around the edges.

To reheat: Spread the slices on a parchment lined baking sheet and heat in a 350 degrees F oven for about 5 minutes.

Measure all the ingredients into a small glass jar with a tight-fitting lid. Screw on the lid and shake the contents vigorously. The vinaigrette keeps in the refrigerator for a week. Bring to room temperature and shake vigorously again before using.