Wash the rice in several changes of water, and drain. Beat the egg yolks in a bowl for 1–2 minutes. Beat the whites until stiff.
Heat the milk in a saucepan until it almost boils. Put in the rice, stir once, and leave it to simmer until all the milk has been absorbed by the rice (this takes about 15 minutes). Take the pan off the heat, stir in the butter, and set aside to cool.