Preheat oven to 425F.
Toss the beets with 1 teaspoon olive oil and season with salt and pepper. Arrange in one third of an oven proof skillet. Repeat with the carrots and parsnips. Scatter the garlic over the vegetables.
Set the skillet over high heat until you hear it begin to sizzle, about 5 minutes. Cover and transfer to the oven. Roast for 35 minutes, or until tender.
In a second skillet, heat 1 teaspoon oil over medium heat. Add the shallot and cook until softened, about 1 minute. Add the beet greens and cook until wilted, about 5 minutes.
While the vegetables roast, whisk together the vinegar, remaining oil, and half of the shallot. Stir in the cheese.
Toss together the vegetables and the greens. Drizzle the vinaigrette over the dish and season with salt and pepper. Serve warm.