Preheat oven to 400 degrees F.
Place the carrots and parsnips on a large rimmed baking sheet and drizzle generously with olive oil, about 3 tablespoons. Sprinkle generously with salt and pepper, the sprigs of Thyme. Toss everything together, so the veggies are well coated with the olive oil and seasonings.
Roast for about 30 – 40 minutes. Every once in awhile stir the veggies, so they roast evenly on all sides.
When the veggies are softened and caramelized, remove from oven. Serve warm or room temperature.