Place the whole head of cabbage in boiling water for about 2 minutes until the leaves loosen; carefully remove leaves and let them cool.
Heat your oven to 350°F (175°C).
Cook the rice slightly less than package directions by about 5 minutes; set aside.
In a skillet, sauté ground pork or turkey, ground beef, diced onions, minced garlic, and seasonings until meats are cooked through and no pink remains; drain excess fat.
Combine the cooked rice, diced tomatoes with juices, and ⅓ cup of tomato sauce with the meat mixture; stir in the egg until fully incorporated.
Mix together the remaining tomato sauce and the condensed tomato soup in a bowl.
Trim or thin out any thick stems from the cabbage leaves; place about ¼ to ⅓ cup of filling on each leaf, fold in sides, and roll tightly; position them seam side down in a 9x13-inch baking dish coated lightly with the tomato sauce mixture.
Cover the cabbage rolls with the remaining sauce from the bowl, cover the dish tightly with foil, and bake for 75 to 90 minutes.
Allow the cabbage rolls to cool for 15 minutes before serving to let flavors meld.