Remove the core from the cabbage head and submerge the entire head in a large pot of boiling water. Boil for 3-5 minutes until outer leaves soften; peel them off and repeat until approximately 12-14 large leaves are removed.
Using a paring knife, shave down the thick central vein on the back of each cabbage leaf to make it flexible for rolling.
In a large mixing bowl, combine the ground beef, ground pork, cooked rice, onion, garlic, egg, salt, pepper, and marjoram until evenly distributed.
Place approximately 1/4 cup of the meat mixture at the base of a cabbage leaf. Fold the sides inward and roll the leaf tightly towards the top.
Line the bottom of a large Dutch oven with any remaining or torn cabbage leaves to create a non-stick barrier.
Arrange the cabbage rolls seam-side down in the Dutch oven, fitting them tightly together in layers.
In a separate bowl, whisk together the tomato sauce, crushed tomatoes, brown sugar, lemon juice, and beef broth.
Pour the sauce mixture evenly over the cabbage rolls.
Cover the pot and simmer over low heat for 90 minutes, or until the cabbage is tender and the internal temperature of the filling reaches 160°F (71°C).
Remove from heat and let rest for 10 minutes before serving to allow the sauce to thicken slightly.