Preheat the oven to 425°F. Cut carrots and parsnips into 2-inch lengths, halving as needed so that all the pieces are about the same size. Add salt and pepper, and toss in a large bowl. Melt butter and add the brown sugar and vinegar, then pour over vegetables and toss to coat. Spoon into a large shallow baking dish (large enough so that the parsnips and carrots are only one layer deep). Bake for 20 minutes. Remove the pan from the oven and stir in the thyme. Continue to bake until the parsnips are lightly browned and tender when pierced with a fork, 10-15 minutes longer.
Adapted from The Herbfarm Cookbook by Jerry Traunfeld