01 - Preheat oven to 375°F. Lightly grease a 9x13-inch baking dish with cooking spray or a small amount of oil.
02 - Bring a large pot of salted water to a boil. Cook pasta shells or penne for 2 minutes less than package directions for al dente texture. Drain thoroughly and set aside.
03 - In a large skillet over medium heat, warm olive oil. Add diced onion and cook for 3 minutes until translucent and softened. Add minced garlic and cook for 1 minute until fragrant, being careful not to burn.
04 - Add ground beef to the skillet. Cook for 5-6 minutes, breaking apart with a wooden spoon, until thoroughly browned and no pink remains.
05 - Stir chopped cabbage into the beef mixture. Sauté for 5-7 minutes, stirring occasionally, until cabbage is wilted and tender-crisp.
06 - Add crushed tomatoes, tomato sauce, tomato paste, dried oregano, dried basil, smoked paprika, and sugar (if using). Stir well to combine. Reduce heat to low and simmer for 10 minutes to allow flavors to meld. Season generously with salt and pepper to taste.
07 - In a large bowl, combine cooked pasta, beef-cabbage sauce mixture, and half of the shredded mozzarella cheese. Gently fold together until evenly incorporated.
08 - Transfer the pasta mixture to the prepared baking dish, spreading evenly. Top with remaining mozzarella cheese and all of the grated Parmesan cheese in an even layer.
09 - Cover the baking dish tightly with aluminum foil. Bake for 20 minutes to heat through and allow flavors to blend.
10 - Remove foil and return to oven for an additional 10 minutes, or until cheese is fully melted, bubbly, and golden brown on top.
11 - Remove from oven and let the dish rest for 5 minutes before serving. This allows the cheese to set slightly and makes serving easier.