Rinse the rice under cold water in a fine-mesh sieve until the water runs clear.
Add the rice, water, cinnamon stick and lemon peel to a heavy-bottomed pan. Bring to the boil over a medium–high heat.
Once boiling, reduce the heat to low, cover and simmer gently for 10–12 minutes, or until the water has been absorbed.
Stir in the milk and sugar, then increase the heat to medium–low and bring to a very gentle simmer, stirring occasionally.
Lower the heat to low and cook, stirring frequently, until the rice is tender and the mixture has thickened, about 25–35 minutes.
Remove from the heat, discard the cinnamon stick and lemon peel, then stir in the vanilla extract.
Serve warm, or transfer to a bowl to cool and chill if you prefer. Sprinkle with ground cinnamon to serve.