Preheat your oven to 350°F (175°C).
In a large skillet over medium heat, brown the ground beef with the diced onion and minced garlic until the beef is fully cooked. Drain any excess fat.
Stir in the chopped cabbage, diced tomatoes, tomato sauce, uncooked rice, beef broth, oregano, paprika, salt, and black pepper. Mix well to combine all ingredients.
Bring the mixture to a simmer, then cover and cook for about 10 minutes, stirring occasionally, until the cabbage is tender.
Transfer the mixture to a greased 9x13-inch baking dish. If using, sprinkle the shredded cheddar cheese evenly over the top.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 15 minutes, or until the cheese is melted and bubbly.
Let the casserole cool for a few minutes before serving.