Cook the rice in the milk until thoroughly dry; add the butter, 5 tablespoons cheese, the salt, pepper, and nutmeg and mix well with a fork.

Using your hands, form the rice mixture into a series of Ping-Pong- size balls; roll each in flour and dip into the beaten egg. Fry them in hot oil until all sides are browned; drain on paper towels.

Heat the chicken broth to boiling.

Arrange from 5 to 6 rice balls per soup bowl, pour the hot broth over then, and serve hot topped with grated cheese to taste.