1. Heat the olive oil in a large deep skillet over medium-high heat. Add the ground beef and cook, breaking it into crumbles, until it is mostly browned.

2. Stir in the diced onion and cook for 3–4 minutes, until the onion is softened and translucent.

3. Add the minced garlic and cook for 30 seconds, just until fragrant. Spoon off any excess grease from the pan if needed.

4. Sprinkle the salt, black pepper, smoked paprika, dried oregano, dried thyme, and crushed red pepper flakes (if using) over the beef mixture. Stir well so the seasonings evenly coat the meat.

5. Stir in the tomato paste and cook for 1 minute to toast it and deepen the flavor.

6. Add the diced tomatoes with their juices, the tomato sauce, and the beef broth. Stir to combine, bring the mixture to a gentle simmer, and cook for 5–7 minutes until slightly thickened.

7. Reduce the heat to low. Add the cooked white rice and stir until the rice is evenly coated in the tomato beef sauce and no dry clumps remain.

8. Add 1 1/2 cups of the shredded cheddar cheese to the skillet, reserving the remaining 1/2 cup for topping. Stir until the cheese is melted and the mixture is creamy and well combined. Taste and adjust seasoning if desired.

9. Preheat the oven to 375°F (190°C). Spread half of the chopped green cabbage into the bottom of a 9×13-inch baking dish in an even layer.

10. Spoon half of the beef and rice mixture over the cabbage and gently spread it from edge to edge.

11. Add the remaining cabbage in an even layer over the beef mixture, then top with the rest of the beef and rice mixture, smoothing the surface so the casserole bakes evenly.

12. Cover the baking dish tightly with foil and bake for 30 minutes, or until the cabbage is mostly tender and the casserole is bubbling around the edges.

13. Remove the foil, sprinkle the remaining 1/2 cup shredded cheddar cheese evenly over the top, and return the casserole to the oven. Bake uncovered for 10–15 minutes, until the cheese is melted, lightly browned, and the cabbage is fully tender.

14. Let the casserole rest for 10 minutes before serving so the layers can set and are easier to scoop.

15. Serve warm, topping each portion with a dollop of sour cream and a sprinkle of chopped fresh parsley, if desired.