Toss carrots, potatoes, shallots, oil, salt and pepper on a large rimmed baking sheet. Roast the vegetables on the highest rack for 1 hour, stirring once. Increase the oven temperature to 425 degrees F. Stir the vegetables again and transfer to the lowest rack. Roast until the vegetables are browned and crisp, about 20 minutes more, stirring once. Toss with balsamic vinegar and transfer to a serving dish.