Heat the olive oil in a large pot over medium heat. Add the ground beef and cook until browned, breaking it apart with a spoon as it cooks.
Stir in the onion and garlic. Cook for 3 to 4 minutes until the onion turns soft.
Add the carrots and cook for 2 more minutes.
Pour in the beef broth. Add the cabbage, diced tomatoes, oregano, salt, and pepper.
Bring the mixture to a boil, then lower the heat and simmer for 20 to 25 minutes until the cabbage is tender.