Preheat the Oven:
Preheat your oven to 350°F (175°C). Grease a 9×13-inch baking dish and set aside.

Prepare the Cabbage:
Bring a large pot of salted water to a boil. Add the chopped cabbage and blanch for about 2-3 minutes, just until tender. Drain and set aside.

Cook the Ground Beef:
In a large skillet, heat a little oil over medium heat. Add the ground beef, onion, and garlic. Cook, breaking up the meat as it browns, until the beef is cooked through and the onion is soft, about 5-7 minutes.

Combine the Ingredients:
Add the cooked rice, tomato sauce, diced tomatoes, tomato paste, brown sugar (if using), oregano, thyme, salt, and pepper to the skillet with the beef mixture. Stir everything together and let it simmer for 5-10 minutes to allow the flavors to meld.

Assemble the Casserole:
Layer half of the blanched cabbage in the bottom of the prepared baking dish. Top with half of the beef and rice mixture. Repeat with another layer of cabbage and the remaining beef mixture.

Bake:
Cover the casserole with aluminum foil and bake in the preheated oven for 30 minutes. After 30 minutes, remove the foil, sprinkle with shredded mozzarella cheese (if using), and return to the oven for an additional 10-15 minutes, or until the cheese is melted and bubbly.

Serve:
Let the casserole rest for a few minutes before slicing and serving.