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Rinse the medium-grain white rice under cold water in a fine-mesh sieve until the water runs clear.
In a heavy-bottomed saucepan, combine the rinsed rice, water, cinnamon stick, and lemon peel. Bring to a boil over medium-high heat.
Once boiling, reduce heat to low, cover, and simmer gently for 10–12 minutes, or until the water is absorbed.
Pour in the whole milk and add the granulated sugar. Increase heat to medium-low and bring to a very gentle simmer, stirring occasionally.
Reduce heat to low and cook, stirring frequently, until the rice is tender and the mixture thickens, about 25–35 minutes.
Remove from heat. Discard the cinnamon stick and lemon peel, then stir in the vanilla extract.
Serve warm or transfer to a bowl to cool, then chill if desired. Sprinkle ground cinnamon on top before serving.