In a large saucepan, bring rice, sugar, salt and 4 ½ cups milk to a boil over medium heat. Reduce heat to low, cover and let simmer until thickened, about 20 minutes. Stir in vanilla and remaining ¼ cup milk.
Transfer the rice pudding to a serving bowl and cover with cling film, pressing the cling film to the surface of the pudding to prevent a skin from forming on top. Transfer to the refrigerator and leave for about couple of hours.
Before serving, stir in cream, cinnamon, nutmeg and orange zest. Serve with a dollop of fresh whipped cream is desired and top with addition orange shavings.