Preheat the oven to 375°F (190°C) and lightly grease a 9×13-inch baking dish.
Bring a large pot of salted water to a boil. Add the chopped cabbage and cook for 5–7 minutes until slightly tender. Drain thoroughly and gently remove as much moisture as possible.
Heat the butter and olive oil in a large skillet over medium heat. Cook the onion until softened, then stir in the garlic and cook for 30 seconds.
Add the ground beef and cook until browned, breaking it into small crumbles. Drain excess grease and season with Italian seasoning, paprika, salt, and black pepper.
In a large bowl, whisk together the eggs and sour cream. Stir in the cheddar cheese, half of the mozzarella, Parmesan cheese, and parsley.
Fold the cooked cabbage and seasoned beef into the creamy cheese mixture until evenly combined.
Transfer the mixture into the prepared baking dish and spread evenly. Sprinkle with the remaining mozzarella cheese.
Mix the breadcrumbs, melted butter, and Parmesan cheese together if using, then sprinkle evenly over the casserole.
Bake uncovered for 30–35 minutes until the casserole is bubbling and the cheese is melted. Broil for 2–3 minutes for a golden-brown topping if desired.
Allow the casserole to rest for 10 minutes before serving. Garnish with fresh parsley and enjoy.