Bring water and rice to a boil in a saucepan. Immediately reduce heat to medium-low. Simmer uncovered very slowly, stirring occasionally, until most of the water has been absorbed and rice is soft, about 30 minutes.

Pour 2 cups milk and sugar into the saucepan and increase heat to high.

Meanwhile, stir together 1/2 cup milk and cornstarch in a bowl.

Once rice-milk mixture is boiling, add cornstarch mixture and vanilla extract. Stir until well combined. Remove from heat.

Ladle rice pudding into individual serving dishes and sprinkle with cinnamon. Allow to cool to room temperature. Refrigerate until well chilled, at least 4 hours.