Preheat the oven to 375 degrees. Lightly grease a 9-by-13-inch baking dish.
Brown the ground beef in a large skillet over medium heat, breaking it up as it cooks. Add the diced onion and minced garlic and cook until the onion softens.
Stir in the uncooked rice, paprika, oregano, salt, and black pepper. Cook for one minute so the rice gets coated with the seasonings.
Add one cup of tomato sauce and one cup of beef broth to the skillet. Simmer for five minutes, then remove from heat.
Spread half the chopped cabbage in an even layer in the prepared baking dish. Spoon the beef and rice mixture over the cabbage. Top with the remaining cabbage.
Pour the rest of the tomato sauce and beef broth over the top, spreading it gently so the liquid reaches the bottom layer.
Cover the dish tightly with foil and bake for 45 minutes. Remove the foil and bake for 15 more minutes until the rice is tender and the cabbage is soft.