In a saucepan bring milk and cinnamon stick to a simmer. Stir in the rice and bring to a boil.

Reduce heat and simmer over very low heat for 30 minutes, stirring occasionally. Using a vegetable peeler, remove the zest in strips from the lemon and finely chop. Remove the cinnamon stick. Add the lemon zest and sugar and continue to simmer for another 45 minutes until thick and creamy. Add the heavy cream to adjust the pudding's consistency, if desired. Serve warm.