In a heavy saucepan, bring the milk and the cinnamon stick to a simmer.
Stir in the rice and bring to a boil. Reduce the heat and simmer for about 30 minutes over very low heat, stirring occasionally.
Using a vegetable peeler, remove the zest from the lemon in strips. Chop the zest very fine.
Remove the cinnamon stick and add the lemon zest and sugar. Continue to simmer for another 45 minutes, or until the mixture has become very thick and creamy.
Add the heavy cream, if desired, to adjust the consistency of the pudding. Serve warm.