Heat the olive oil in a large pot over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Stir in the onion and garlic. Cook for 3 minutes until the onion softens.
Add the rosemary, salt, and pepper. Stir for 30 seconds to release the herb aroma.
Pour in the beef broth. Add the carrots and potatoes. Bring to a boil, then reduce to a simmer. Cover and cook for 15 minutes.
Add the green beans. Simmer uncovered for another 10 minutes until the vegetables are tender but the beans still have some bite.
Taste and adjust salt if needed before serving.