How to Make It
Preheat oven to 450°F. Line 2 rimmed baking sheets with parchment paper, and lightly coat with cooking spray.
Combine onions, purple sweet potatoes, purple carrots, and 2 tablespoons olive oil in a large bowl; toss to coat, and arrange in a single layer on a prepared baking sheet. In the same bowl, combine turnips, parsnips, remaining carrots, and remaining 2 tablespoons olive oil, and toss to coat; arrange in a single layer on the other prepared baking sheet. Sprinkle both baking sheets of vegetables evenly with salt and pepper. Bake purple vegetable mixture at 450°F, without stirring, until tender, about 25 minutes. Bake turnip mixture at 450°F, without stirring, until tender and lightly caramelized, 30 to 35 minutes.
While vegetables bake, combine vinegar and syrup in a small saucepan over medium-high. Bring to a boil, without stirring, and cook until mixture is thickened, 6 to 8 minutes. (You should have about 1/2 cup of liquid.) Remove from heat, and cool to room temperature; sauce will thicken to syrupy consistency upon cooling.
Arrange roasted vegetables on a platter, and drizzle with balsamic syrup. Sprinkle with fresh thyme, and serve immediately.