Heat oil in Dutch oven over medium-high heat. Place roast in pan and sear on all sides until brown.
Add onions, garlic and carrots to pan and stir. Cook until onions begin to brown. Add wine to deglaze pan.
Add beef broth and fresh herbs last to Dutch oven. Cover with lid. Place into oven and cook until roast is fall-apart tender, easily shredded using a fork. Approximately 3 hours for a 3-lb roast and 4 hours for a 4- to 5-lb roast.
For crock pot cooking, transfer everything to crock pot before beginning step 5. Cook on low until fall-apart tender, approximately 6-8 hours. Cooking on a higher setting will result in a tougher roast.