Cut the core out of the cabbage using a knife. Place the cabbage (minus the core) into a large pot of salted boiling water. Cook for about 12-14 minutes until the leaves can be gently pulled off without tearing. Remove 8 large leaves for rolling and set aside additional leaves for lining the baking dish.
Line the bottom of an 11x8 baking dish with the leftover cabbage leaves to prevent sticking.
Preheat your oven to 350°F (175°C).
In a medium saucepan, bring 2/3 cup water to a boil. Add the rice, cover, and simmer for 20 minutes until cooked through.
Prepare the sauce by mixing both cans of tomato soup with brown sugar and Worcestershire sauce in a small bowl.
In a large mixing bowl, combine the ground beef, cooked rice, chopped onion, beaten egg, salt, black pepper, and 1/4 cup of the tomato soup mixture. Stir everything together thoroughly.
Lay out the 8 reserved cabbage leaves on a clean surface. Spoon an equal amount of the beef mixture into the center of each leaf. Roll each leaf up firmly and secure it with a toothpick.
Arrange the rolled cabbage rolls seam-side down over the cabbage-lined baking dish.
Pour the remaining tomato soup mixture evenly over the cabbage rolls. Cover the top with several remaining cabbage leaves, then seal the dish tightly with aluminum foil.
Bake in the preheated oven for 90 minutes, or until the meat filling is completely cooked. Remove from the oven and serve warm.