Preheat oven to 300°.
Trim fat from roast. Heat oil in a Dutch oven over medium-high heat until hot. Add roast; brown on all sides. Remove roast; set aside. Add chopped onion to pan; sauté 3 minutes. Add thyme, garlic, and bay leaves; sauté 1 minute. Add broth, wine, and canned tomatoes, scraping pan to loosen browned bits. Return roast to pan; sprinkle with salt and pepper. Cover and bake at 300° for 1 hour.
Remove from oven; turn roast over. Add carrots, boiling onions, and sun-dried tomatoes. Cover; bake 1 hour. Add mushrooms. Cover; bake an additional hour or until roast is very tender. Let stand 10 minutes. Thinly slice roast and serve with vegetables.