In a large skillet, heat the 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. Add the garlic and continue cooking for 1 minute.
Add the chopped cabbage, tomatoes with juice, tomato sauce, pepper, and salt. Bring to a boil. Cover, reduce heat and simmer for 20 to 25 minutes, or until cabbage is tender.
Pour soup in individual bowls over hot cooked rice.