Heat a pot over medium heat. Add in the ground beef, brown the beef while breaking it up into smaller pieces with a spatula. When its halfway browned add in the onion, carrot, celery, and garlic. Season with salt and pepper and saute for 3 to 4 minutes.
Once the beef is browned add in the crushed tomato, broth, and rosemary.
Partially cover with a lid and bring to a simmer for about 35 minutes. Remove the lid and add in the green beans. Simmer for 5 - 7 minutes. Taste and adjust the seasoning with salt if needed.
Portion a balanced amount of meat and vegetables to broth into a bowl and serve with bread.