Dice the onion into small pieces and mince the garlic. Shred the carrot and chop the cabbage into 1-inch squares. Measure out all seasonings (paprika, Cajun spice, salt, pepper), tomato sauce, diced tomatoes, Worcestershire sauce, sugar, and mozzarella cheese. Preheat your oven to 350°F and lightly grease a 9x13 inch baking dish or similar size casserole.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the diced onion and shredded carrot, cooking for about 2 minutes until the onion begins to soften. Add the ground beef and cook, breaking it apart with a spoon, until it's completely browned and no pink remains (about 5-7 minutes). Stir in the minced garlic and cook for 1 minute more until fragrant. Drain off excess liquid if needed, then add the Worcestershire sauce, sugar, paprika, Cajun spice, salt, and pepper. Stir in the tomato sauce and diced tomatoes, then simmer on medium-low heat for 10 minutes to let the flavors develop and meld together. I like to taste the sauce at this point and adjust the seasonings—a pinch more salt can really bring out the depth of flavor.
While the beef sauce simmers, heat 1 tablespoon of olive oil in another skillet over medium heat. Add the chopped cabbage and 1/4 cup water, then cook, stirring occasionally, until the cabbage is softened and wilted (about 8-10 minutes). The water helps steam the cabbage while the oil prevents sticking. Season lightly with salt and pepper to taste.
Once the beef sauce has simmered for 10 minutes, add the 1.5 cups of cooked rice to the skillet and stir until everything is well combined and heated through. The rice will absorb some of the sauce flavors and add substance to the casserole filling.
Spread half of the cooked cabbage from Step 3 evenly across the bottom of the prepared baking dish. Top with half of the beef and rice mixture from Step 4, spreading it in an even layer. Repeat with the remaining cabbage, followed by the remaining beef mixture. This creates balanced layers that will cook evenly and create a hearty, cohesive casserole.
Sprinkle the shredded mozzarella cheese evenly over the top of the casserole. Cover the dish tightly with foil and bake at 350°F for 20 minutes. Remove the foil and bake for an additional 20 minutes until the casserole is bubbling at the edges. For the final step, turn on the broiler and broil for 1-2 minutes, watching closely, until the cheese is melted and lightly browned on top. I find that using pre-shredded mozzarella like Sargento really helps it melt more evenly than freshly shredded cheese.
Remove the casserole from the oven and let it rest for 5 minutes before serving. This allows the layers to set slightly and makes for cleaner portions. Serve hot with your favorite garnishes such as fresh herbs, sour cream, or additional cheese if desired.