Bring a large pot of water to a boil. Core the cabbage and blanch whole, peeling off leaves as they soften, about 2 to 3 minutes per layer. Collect 12 to 14 large leaves and cool on a flat surface. Trim the thick rib from each leaf with a sharp knife.
Heat olive oil in a saucepan over medium heat. Soften diced onion for 5 minutes. Add garlic and tomato paste, cook 1 minute. Add crushed tomatoes, water, sugar, vinegar, paprika, salt, and pepper. Simmer 10 minutes. Taste and adjust seasoning.
In a large bowl, combine ground beef, uncooked rice, grated onion, garlic, egg, tomato paste, salt, pepper, paprika, oregano, and thyme. Mix until just combined.
Preheat oven to 350°F (175°C). Spread a thin layer of sauce on the bottom of a 9x13 inch baking dish.
Place a cabbage leaf flat. Add 3 tablespoons of filling near the bottom edge. Fold up the bottom, fold in the sides, and roll forward firmly. Place seam-side down in the dish. Repeat with remaining leaves and filling.
Pour remaining tomato sauce over and around all the rolls. Cover tightly with aluminium foil.
Bake covered for 1 hour 15 minutes. Remove foil and bake uncovered for 15 more minutes until tops are lightly caramelized and sauce is glossy.
Rest 10 minutes before serving. Serve with fresh parsley, a dollop of sour cream, and crusty bread.