For the vegetables: Preheat the oven to 425°F. Put the oven rack in the top third of the oven. Line a baking sheet with foil or grease with olive oil.
In a large bowl, combine the oil, sweet potato, carrots, parsnips, onion, garlic, and thyme. Season liberally with salt and pepper and toss to coat. Transfer to the prepared baking sheet.
Roast, turning once halfway through, until the vegetables are tender and starting to brown, about 45 minutes.
For the vinaigrette: Meanwhile, in a small bowl, whisk together the oil, vinegar, mustard, honey, and shallot. Season to taste with salt and pepper.
Transfer the roasted vegetables to a serving bowl and toss with the vinaigrette. Serve warm.