Bring a large pot of water to a boil and simmer the whole cabbage for several minutes until the leaves soften and can be removed easily. Allow the leaves to cool before handling so they remain flexible and easy to roll.
In a mixing bowl combine ground beef, ground pork, cooked rice, chopped onion, minced garlic, egg, parsley, salt, pepper, and paprika. Mix gently until the ingredients are evenly distributed without compacting the meat mixture.
Place a cabbage leaf flat on the work surface, add a portion of filling near the base, fold the sides inward, and roll tightly upward. Repeat until all cabbage leaves and filling are used.
Prepare the sauce by heating olive oil and stirring in crushed tomatoes, tomato sauce, tomato paste, sugar, salt, pepper, and oregano. Simmer the sauce briefly until it thickens slightly and the flavors combine.
Arrange the cabbage rolls seam-side down in the sauce, add beef broth, cover, and simmer slowly until the cabbage becomes tender and the filling cooks through.
Let the cabbage rolls rest for a few minutes before serving so the juices redistribute inside the filling and the sauce settles around the rolls.
