Brown the beef in a skillet over medium-high heat with the onion until the meat is cooked through. Drain excess fat. Stir in garlic and cook 30 seconds.
Add chopped cabbage to the slow cooker. Scatter diced bell pepper over the cabbage if using.
Spoon the browned beef mixture over the cabbage.
In a bowl, stir diced tomatoes, tomato sauce, rice, Worcestershire, brown sugar, paprika, salt, and pepper. Pour evenly into the slow cooker.
Stir gently to combine, pressing cabbage down so it's mostly covered by sauce.
Cook on LOW for 6–7 hours or HIGH for 3–4 hours, until cabbage is very tender and rice is cooked.
Sprinkle cheese over the top, cover, and cook 10–15 minutes until melted.
Spoon into bowls and sprinkle with parsley.
