Brown the ground beef and onion in the olive oil, then add the garlic and cook briefly.
Combine the tomatoes, tomato sauce, broth, Worcestershire sauce, tomato paste, and seasonings.
Add the beef mixture, rinsed rice, and cabbage to a 6-quart slow cooker and stir to combine.
Cover and cook on LOW for 7 to 8 hours or HIGH for 4 to 5 hours, until the rice and cabbage are tender and the beef reaches 160°F.
Top with cheddar, cover, and cook until melted, then rest the casserole for 10 minutes.
Garnish with parsley and serve hot.