Place onions in a medium saucepan, and cover with water. Bring to a boil, and cook 1 minute. Drain and plunge onions into ice water. Drain and peel.
Place onions, carrots, and potatoes in a broiler pan. Add rosemary and next 4 ingredients; toss to coat. Bake at 475° for 35 minutes, stirring after 17 minutes.
Place vegetables in a serving bowl. Add flat-leaf parsley and balsamic vinegar; toss gently.
Cipollini: We found cipollini ("little onions") in a variety of supermarkets as well as specialty stores. They are small, round, flat onions that have a touch of sweetness. We also tested with two small Vidalia onions, chopped, and liked the flavor as well. To easily remove the skins from cipollini onions, boil them for 1 minute, and then plunge then into an ice-water bath. The skins will slip off easily.