Preheat oven to 325°.
Heat oil in a large Dutch oven over medium-high heat. Sprinkle roast evenly with salt and pepper. Add roast to pan; cook 8 minutes or until browned on all sides. Remove roast from pan.
Add onion and garlic to pan, and sauté 6 minutes or until tender. Return roast to pan. Add broth, wine, and thyme to pan; bring to a simmer. Cover and bake at 325° for 1 hour.
Add carrot and next 3 ingredients to pan. Cover and bake an additional 3 1/2 hours or until vegetables and roast are tender. Remove roast and vegetables to a serving dish, reserving juices in pan; discard thyme sprigs.
Combine flour and 1/2 cup pan juices in a small bowl, stirring with a whisk. Return mixture to pan. Bring to a simmer over medium heat; cook 15 minutes or until thick. Slice or shred roast; serve with vegetables and gravy.