Preheat your oven to 325°F (165°C).
Trim any large pieces of excess fat from the beef chuck roast and pat it dry with a paper towel.
In a small bowl, combine the olive oil, sea salt, black pepper, rosemary, thyme, and minced garlic to create a herb paste.
Rub the herb paste evenly over all sides of the beef.
Place the beef in a small Dutch oven or oven-safe roasting dish.
Arrange the sliced carrots around the beef and pour the beef broth into the bottom of the dish.
Cover the dish tightly with a lid or aluminum foil and roast for 2.5 to 3 hours, or until the beef is extremely tender and easily pulls apart with a fork.
While the beef rests, steam the green beans for 5-7 minutes until they are bright green and tender-crisp.
Slice or shred the beef and serve alongside the roasted carrots and steamed green beans, drizzling any remaining pan juices over the top.