Bring a large pot of salted water to a boil and carefully remove the core from the cabbage head using a sharp knife. Submerge the whole cabbage in the boiling water for 5 to 7 minutes, peeling off the leaves with tongs as they soften. Set the softened leaves aside on a paper towel-lined plate to drain and cool.

Preheat your oven to 350°F (175°C). In a medium bowl, whisk together the crushed tomatoes, tomato sauce, brown sugar, apple cider vinegar, and beef broth to create the braising liquid. Spread about 1 cup of this sauce evenly over the bottom of a 9x13-inch baking dish.

In a large mixing bowl, combine the ground beef, ground pork, cooked rice, chopped onion, minced garlic, egg, salt, and black pepper. Use your hands to mix everything together until just combined, being careful not to overwork the meat to keep it tender.

Take a cooled cabbage leaf and use a paring knife to shave down the thick center rib so it folds easily. Place about 1/4 cup of the meat mixture at the bottom of the leaf, fold the sides in, and roll it up tightly like a burrito. Place the roll seam-side down in the prepared baking dish, and repeat until all the meat mixture is used.

Pour the remaining tomato sauce evenly over the stuffed cabbage rolls in the baking dish, ensuring they are well coated. Cover the dish tightly with aluminum foil to trap the steam and keep the cabbage moist.

Bake in the preheated oven for 75 to 90 minutes, or until the cabbage is completely tender and the meat is cooked through to an internal temperature of 160°F. Remove the foil for the last 15 minutes of baking to let the sauce bubble and thicken slightly.

Let the stuffed cabbage rest for 10 minutes before serving so the rolls set up and hold their shape. Garnish with fresh chopped parsley and serve warm with a dollop of sour cream or crusty bread to soak up the rich tomato sauce.