In a saucepan, heat the water and rice. Season with a little salt and cook until dry.
After the water has evaporated, add the butter, the lemon peel, the cinnamon sticks and the milk. Stir and cook for 30 minutes. Stir from time to time to prevent it from sticking to the bottom. After 30 minutes, add the sugar.
Dissolve the egg yolks with the cup of milk. While stirring, add the egg yolks to the rice and when they start to bubble, remove from the heat.
After filling bowls, put the rice pudding in the fridge. When cold, sprinkle with cinnamon and serve.