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Rinse the rice under cold water in a fine-mesh sieve until the water runs clear.
Combine the rinsed rice, 2 cups water, cinnamon stick, and lemon peel in a heavy-bottomed saucepan and bring to a boil over medium-high heat.
Reduce heat to low, cover, and simmer gently until the water is absorbed, about 10–12 minutes.
Pour in the whole milk and stir in the granulated sugar; increase heat to medium-low and bring to a very gentle simmer.
Reduce heat to low and continue cooking, stirring frequently, until the rice is tender and the mixture has thickened, about 25–35 minutes.
Remove from heat, discard the cinnamon stick and lemon peel, and stir in the vanilla extract.
Serve warm or transfer to a bowl to cool, then chill in the refrigerator; sprinkle ground cinnamon on top before serving.