Add the chopped cabbage, tomatoes, tomato sauce, pepper, and salt. Bring to a boil. Cover and simmer for 20 to 30 minutes, or until cabbage is tender.
Add the garlic and continue cooking for 1 minute.
In a large skillet, heat olive oil over medium heat. Add the ground beef and onion and cook, stirring, until ground beef is no longer pink and onion is tender.