Step 1: Prepare the cabbage. Carefully remove the core from the cabbage head. Bring a large pot of salted water to a boil. Submerge the whole cabbage head in the boiling water for 5-10 minutes, or until the outer leaves soften and can be easily peeled off. Gently remove the softened leaves, one by one, using tongs. Trim any thick veins from the base of each leaf. Repeat the blanching process as needed until you have enough leaves (around 16-20).
Step 2: Make the filling. In a large skillet, heat olive oil over medium heat. Add chopped onion and cook until softened, about 5-7 minutes. Add minced garlic and cook for another minute until fragrant. Transfer onion and garlic to a large mixing bowl.
Step 3: Add ground beef, ground pork, cooked rice, beaten egg, salt, pepper, paprika, and marjoram to the bowl with the onion mixture. Using your hands, gently but thoroughly mix all ingredients until well combined, being careful not to overmix.
Step 4: Assemble the cabbage rolls. Lay a prepared cabbage leaf flat. Place about 1/4 to 1/3 cup of the meat mixture near the stem end of the leaf. Fold the sides of the leaf over the filling, then roll tightly from the stem end towards the top, creating a neat parcel. Repeat with remaining leaves and filling.
Step 5: Prepare the sauce. In a large Dutch oven or oven-safe pot, combine crushed tomatoes, tomato sauce, water or beef broth, brown sugar (if using), and apple cider vinegar (if using). Stir well to combine.
Step 6: Arrange the rolls. Carefully place the assembled cabbage rolls seam-side down in a single layer in the prepared sauce. If necessary, you can arrange them in two layers. Ensure they are mostly submerged in the sauce.
Step 7: Cook the cabbage rolls. Cover the pot and bake in a preheated oven at 350°F (175°C) for 1 hour 30 minutes to 2 hours, or until the cabbage is very tender and the filling is cooked through. Alternatively, simmer gently on the stovetop over low heat for 1.5-2 hours.
Step 8: Rest and serve. Once cooked, let the cabbage rolls rest for 10-15 minutes before serving. This allows the flavors to meld and the rolls to firm up slightly. Serve hot, with extra sauce.