Soak the bread in the milk in a small bowl until it is thoroughly moist, about 5 minutes. Squeeze the bread dry and crumble it into a larger
bowl. Add ground beef, 1/4 cup Parmesan cheese, egg, parsley, salt and pepper. Mix well and form into marble-size balls, about 60 in number. Place them on waxed paper or on a plate.
Detach all the leaves from the head of the escarole and discard any that are bruised, wilted or discolored. Wash all the rest in various changes of cold water until thoroughly clean. Cut into ribbons and set aside.
Cook escarole in a pot of boiling salted water for about 5 minutes. Drain in a colander, then rinse under cold running water. Drain again and set aside.
Cook basmati rice according to package directions.
Bring broth to a boil in a large soup pot. Add the meatballs, reduce the heat to medium and simmer, covered, about 5 minutes. Add the escarole and cook, partially covered, until the meatballs are cooked, about 5 minutes more. Add the rice and serve hot.
Pass the extra grated Parmesan cheese for topping the soup.