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