Preheat oven to 475°F. Line a rimmed baking sheet with foil or parchment paper.
Cut carrots and parsnips in half lengthwise and into 2-inch or 3-inch lengths and so all pieces are same thickness. Toss carrots and parsnips with 2 Tbsp. oil, season with salt, and spread in a single layer on prepared baking sheet. Roast until vegetables begin to brown, 20 to 25 minutes, shaking pan 2 or 3 times during cooking time.
Mix remaining oil, garlic and thyme. Remove baking sheet from oven; drizzle mixture over vegetables and toss. Roast until vegetables are well-browned, 5 minutes more.