In a large pot, add in the milk, rice, sugar, orange slice, vanilla and cinnamon stick. Bring this mixture to an almost boil and lower heat to a simmer. Allow the mixture to cook on LOW heat, stirring constantly, until it thickens and the rice is cooked - about 30 minutes total time. STAY ON TOP OF THIS POT THE WHOLE TIME. It will bubble over if left unattended. Also, use a skimmer spoon to remove most of the 'skin' that the milk produces from the top of the mixture.
Discard the cinnamon stick and orange peel and then transfer portions to four small bowls and sprinkle with cinnamon. Serve warm or allow the pudding to come to room temperature and then cover and refrigerate.