01 - Set oven to 375°F. Lightly grease a 9x13-inch baking dish with a neutral oil or spray.
02 - Bring a large pot of heavily salted water to a boil. Cook the pasta two minutes less than package instructions indicate. Drain well and reserve.
03 - In a large skillet over medium heat, warm olive oil. Add diced onion and cook for 3 minutes until translucent. Stir in minced garlic and cook 1 minute more until fragrant.
04 - Add ground beef to skillet. Cook, breaking up the meat with a spoon, until well browned and no pink remains, about 5 to 6 minutes.
05 - Incorporate chopped cabbage into the skillet. Sauté, stirring occasionally, until cabbage softens, about 5 to 7 minutes.
06 - Add crushed tomatoes, tomato sauce, tomato paste, dried oregano, basil, smoked paprika, and sugar if using. Reduce heat and simmer uncovered for 10 minutes. Adjust salt and pepper to taste.
07 - In a large mixing bowl, gently toss cooked pasta with beef-cabbage-tomato mixture and half of the shredded mozzarella cheese. Mix just until evenly distributed.
08 - Transfer mixture to prepared baking dish. Spoon evenly and sprinkle with remaining mozzarella and all the grated Parmesan cheese.
09 - Cover dish tightly with foil and bake 20 minutes. Remove foil and continue baking 10 minutes or until cheese is bubbling and lightly golden.
10 - Allow to rest at room temperature for 5 minutes before serving to help set layers.