Combine the rice, water, lemon peel, and cinnamon stick in a heavy saucepan. Bring to a simmer and cook until the water is almost absorbed, about 15 minutes.
Warm the milk separately, then gradually stir it into the rice.
Make the Custard:
Add the sugar and cook over low heat for 20 minutes, stirring often, until creamy and tender.
Whisk the egg yolks and vanilla in a bowl. Slowly whisk in a cup of hot pudding, then return the mixture to the saucepan.
Cook for 2 to 3 minutes without boiling, until lightly thickened.
Chill and Serve:
Remove the lemon peel and cinnamon stick. Spoon the pudding into shallow bowls.
Cool slightly or chill completely, then dust with cinnamon before serving.
Notes
The pudding thickens as it cools, so remove it from the heat while it is still spoonable.
Use a vegetable peeler for a clean lemon strip without bitter white pith.