Scrub potatoes and carrots. Cut potatoes in half. Peel onions. In a 12- by 15-inch roasting pan, mix potatoes, carrots, onions, oil, thyme, rosemary, and pepper.
Roast vegetables in a 450° oven, stirring occasionally, until tender when pierced, 40 to 50 minutes.
Transfer pan from oven to rangetop and set over medium heat. Add red wine, balsamic vinegar, and chicken broth. Stir until brown drippings are scraped free and vegetables are coated, 2 to 4 minutes.
Spoon vegetables into a bowl. Add salt to taste.
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