Preheat oven to 425°. Toss carrots, parsnips, turnips, and brussels sprouts in a large bowl with 3 tablespoons oil. Transfer to a rimmed baking sheet; sprinkle with salt and pepper. Roast for 30 minutes. Add sun-dried tomatoes, toss, and return to oven. Continue to roast until vegetables are tender and beginning to brown, tossing often, 30–45 more minutes. (If brussels sprouts are cooking too quickly, move them to pan center and move root vegetables toward edges.)