Preheat oven to 375°F and grease a 9x13" baking dish.
In a skillet over medium heat, brown ground beef with diced onion and garlic. Drain any grease.
Add tomato sauce, diced tomatoes, broth, paprika, salt, and pepper. Simmer for 5–7 minutes.
While sauce simmers, lightly sauté chopped cabbage in a separate skillet until slightly tender.
Begin layering in the baking dish: start with cabbage, then beef mixture, then rice. Repeat and finish with sauce on top.
Cover with foil and bake for 45–50 minutes. Uncover, top with cheese, and bake an additional 10 minutes.
Let rest for 10 minutes before serving.