Preheat your oven to 350°F (175°C).
In a large skillet, cook the ground beef over medium heat until browned. Drain any excess fat.
Add the chopped onion and minced garlic to the skillet. Cook until the onion is translucent.
Stir in the tomato sauce, diced tomatoes, uncooked rice, beef broth, salt, black pepper, paprika, and dried thyme. Bring the mixture to a simmer and cook for about 5 minutes.
In a greased 9x13 inch baking dish, spread half of the chopped cabbage. Pour half of the beef mixture over the cabbage. Repeat the layers with the remaining cabbage and beef mixture.
Cover the dish with aluminum foil and bake in the preheated oven for 45 minutes. Remove the foil and bake for an additional 15 minutes, or until the cabbage is tender and the casserole is bubbly.
If using, sprinkle the shredded mozzarella cheese over the top of the casserole during the last 10 minutes of baking.
Let the casserole cool for a few minutes before serving. Garnish with fresh parsley.