Make vinaigrette; whisk together balsamic vinegar, walnut oil, and 1 tablespoon olive oil; set aside.
Heat oven to 400 degrees F.
Remove stems and leafy greens from tops of beets; reserve greens, and discard stems. Rinse greens thoroughly and refrigerate. With a firm bristle vegetable brush or the back of a paring knife, scrub beets clean under cold running water. Place beets in a small roasting pan. Add the remaining1 tablespoon olive oil and thyme. Season with salt and pepper. Add enough water to just cover the bottom, cover tightly. Roast for 20 minutes. Uncover and continue to cook until tender to the tip of a sharp knife, about 10 to 15 minutes.
Slice the onions in quarters lengthwise. In a large saute pan over medium low heat, add butter and onions, saute, about 5 to 7 minutes. Reduce heat to medium high and continue cooking until caramelized, about 5 minutes. Transfer the onions to a bowl and set aside.
Remove beet greens from refrigerator. Using the same pan over medium high heat, saute greens just until wilted, about 2 minutes. Transfer immediately to serving plate. Place onions over greens. Trim "tails" from beets and slice larger ones in half. Arrange over wilted greens with onions. Drizzle vinaigrette over beets and greens. Sprinkle with blue cheese. Serve immediately.
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