Rinse orange in hot water, peel orange zest. Break up cinnamon stick.
Rinse rice in colander with cold water.
Melt butter in a saucepan, add rice, sauté briefly and add milk. Add sugar, orange peel, vanilla sugar and cinnamon. Simmer on low heat, covered, for 30-35 minutes or until all liquid has been completely absorbed and rice is cooked. Serve cooled.