Boil a large pot of water. Blanch cabbage leaves 2–3 minutes until flexible. Drain and cool. Trim thick ribs.
Warm olive oil in a skillet over medium heat. Sauté onion until translucent, then stir in garlic for 30 seconds.
Combine ground beef, ground pork, cooked rice, half the onion mixture, parsley, salt, pepper, paprika, and thyme. Mix gently.
Whisk tomato sauce, crushed tomatoes, tomato paste, beef broth, brown sugar, Worcestershire, vinegar, and remaining onions in a bowl.
Spread 1 cup of the sauce in the bottom of the slow cooker.
Spoon about 1/3 cup filling onto a cabbage leaf. Fold sides over and roll snugly. Repeat with remaining leaves and filling.
Arrange rolls seam-side down in the cooker. Pour remaining sauce over the top to cover evenly.
Cover and cook on Low for 6 hours (or on High for 3–4 hours) until the meat is cooked through and tender.
Let rest 10 minutes before serving. Spoon extra sauce over each roll and garnish with parsley if desired.