In a medium saucepan, bring water to a boil. Add rice and stir. Reduce heat, cover and simmer for 20 minutes.
Bring a large, wide saucepan of lightly salted water to a boil. Add cabbage leaves and cook for 2 to 4 minutes or until softened; drain.
In a medium mixing bowl, combine the ground beef, 1 cup cooked rice, onion, egg, salt and pepper, along with 2 tablespoons of tomato soup. Mix thoroughly.
Divide the beef mixture evenly among the cabbage leaves. Roll and secure them with toothpicks or string.
In a large skillet over medium heat, place the cabbage rolls and pour the remaining tomato soup over the top. Cover and bring to a boil. Reduce heat to low and simmer for about 40 minutes, stirring and basting with the liquid often.