Prepare the cabbage: Remove the tough core from the cabbage. Place it in a pot of gently boiling salted water and remove the softened outer leaves one at a time.
Trim the leaves: Lay each leaf flat and carefully trim the thick center rib so it is easier to fold.
Make the filling: Combine ground beef, ground pork, cooled rice, onion, garlic, egg, salt, pepper, marjoram, and paprika. Mix just until combined.
Fill the leaves: Place about 2–3 tablespoons of filling near the bottom of each cabbage leaf. Fold the sides inward and roll it up firmly.
Arrange the rolls: Place a few leftover cabbage leaves in the bottom of a 9×13-inch baking dish. Arrange the cabbage rolls seam-side down.
Make the sauce: Mix crushed tomatoes, tomato sauce, broth, onion, and marjoram. Season to taste.
Add the sauce: Pour the tomato sauce over and around the cabbage rolls.
Bake: Cover tightly with foil and bake at 350°F (175°C) for 1½–2 hours, until the cabbage is tender and the meat is fully cooked.
Rest and serve: Let the rolls rest for about 10 minutes before serving with plenty of tomato sauce.