Set your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish and set it aside.
In a large skillet over medium heat, cook the ground beef until browned, breaking it into crumbles. Drain any extra grease. Add chopped onion and garlic, and sauté for 2–3 minutes until soft and fragrant.
Stir in cooked rice, diced tomatoes, tomato sauce, brown sugar, vinegar, smoked paprika, thyme, salt, and pepper. Simmer for 5 minutes to let the flavors blend.
Spread half of the sliced cabbage into the bottom of the baking dish. Spoon half the beef mixture over the cabbage. Repeat with the rest of the cabbage and beef mixture to create two layers.
Cover tightly with foil and bake for 45–50 minutes, until the cabbage is tender. Uncover during the last 10 minutes if you want a lightly caramelized top.
Let it rest for 5 minutes before serving. Top with chopped parsley, sour cream, or shredded cheese if you’d like. Serve warm.