Bring water and rice to a boil in a saucepan. Reduce heat to low, cover, and simmer until rice is tender and liquid has been absorbed, about 20 minutes.
Meanwhile, 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.
Combine ground beef, 1 cup of cooked rice, onion, egg, 2 tablespoons of tomato soup, salt, and pepper in a large bowl; mix thoroughly.
Spoon about 2 tablespoons of beef mixture onto each cabbage leaf; bring one end of the cabbage leaf over the mixture, rolling and tucking in the ends to prevent the filling from falling out.
Place cabbage rolls in a large skillet over medium heat; pour remaining tomato soup on top. Cover and bring to a boil; reduce heat to low and simmer for about 40 minutes, stirring and basting with the liquid often.
