Preheat oven to 350°.
Combine 1 tablespoon thyme and garlic. Make 12 small slits on outside of beef, and stuff each with about 1/4 teaspoon garlic mixture. Rub beef with 1 teaspoon oil. Sprinkle beef with 1/4 teaspoon salt and 1/4 teaspoon pepper.
Heat a large ovenproof nonstick skillet over medium-high heat. Add beef; cook 2 minutes on all sides or until browned. Remove from pan. Add the chopped onion, chopped carrot, and celery to pan; sauté 6 minutes. Add 1/2 teaspoon salt, broth, wine, vinegar, and bay leaf; bring to a boil. Return beef to pan. Cover and place pan in oven. Bake at 350° for 1 hour. Reduce heat to 325°; turn beef. Cover and bake for an additional 90 minutes or until tender, turning beef twice. Remove beef from pan.
Drain cooking liquid through a sieve into a bowl, pressing down on vegetables to extract liquid. Discard solids. Place a zip-top plastic bag inside a 2-cup glass measure. Pour drippings into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag. Drain drippings into a bowl, stopping before fat layer reaches opening; discard fat.
Trim all but 1 inch from green tops of baby carrots. Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add cipollini onions; sauté 3 minutes or until browned. Add beef, cooking liquid, and baby carrots; bring to a boil. Cover and bake at 350° for 1 hour, turning once. Sprinkle with parsley and 1 teaspoon thyme. Serve the beef with vegetables and sauce.
MyRecipes is working with Let's Move!, the Partnership for a Healthier America, and USDA's MyPlate to give anyone looking for healthier options access to a trove of recipes that will help them create healthy, tasty plates. For more information about creating a healthy plate, visit www.choosemyplate.gov.