Preheat oven to 375 degrees F. Place a sprig of thyme on top of each beet, season with salt and pepper, to taste, and drizzle each beet with 1/4 teaspoon olive oil. Wrap each individually in aluminum foil. Coat bottom of a small cast iron skillet evenly with 1 cup salt. Place skillet in oven, and roast beets until tender enough to be pierced with a sharp knife, 45 minutes to 1 hour. Allow to cool, and peel skin off beets by rubbing with a paper towel.
Quarter leeks lengthwise, without cutting through the root end. Tie leeks together in a bunch with kitchen string.
Prepare an ice bath. Bring medium pot of salted water to a boil. Blanch haricots verts until tender, 5 to 10 minutes. Remove haricots verts from pot with a strainer or slotted spoon, refresh in ice bath, and drain. Blanch leeks in same pot until tender, 10 to 15 minutes. Drain, and cool to room temperature. Cut leeks through the root end, to make 8 quarters; set aside.
Heat remaining 1/2 teaspoon olive oil in a small skillet over medium heat. Add walnuts; toast until fragrant. Season with salt.
On individual plates, thinly slice 1 beet per plate with a mandoline. Season beets with salt and pepper. Arrange haricots verts and leeks on top of beets, then add mache. Drizzle vinaigrette over each salad. Place 2 slices of goat cheese on each salad plate and sprinkle with toasted walnuts. Serve.
In a small bowl, whisk together vinegar, mustard, and grapeseed and walnut oils. Season with salt and pepper.
Yield: about 1/3 cup
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