In a large saucepan, slowly bring the milk, cinnamon stick, strips of lemon rind, and salt to a boil. With a slotted spoon, remove the cinnamon and lemon rind. Stir in the rice and egg yolks, reduce the heat, and allow the rice to simmer for about 15 minutes, stirring constantly.
When the rice is soft, add the sugar and butter and combine well. Pour the mixture into a serving dish, sprinkle with nutmeg, and serve warm.