Heat olive oil in a 6 quart or larger pot over medium heat for a few minutes or until hot. Add ground beef and cook until browned, a few minutes, breaking it apart as it cooks.
Add garlic, salt, oregano, thyme, paprika, and cayenne. Cook until aromatic, about a minute, stirring frequently.
Add all remaining ingredients. Cover with a lid and cook for 10 minutes to soften the cabbage.
Uncover and stir for a minute until well-mixed. Continue cooking uncovered until the cabbage is very tender and nearly all of the liquid has evaporated, about 15 minutes, stirring occasionally. If the pot gets too dry before the cabbage is tender, add beef stock or water as needed.
Serve while hot, optionally garnishing with fresh chopped parsley.