Rinse the rice thoroughly under cold water until the water runs clear. This step is crucial for removing excess starch and preventing a gummy texture.

In a large, heavy-bottomed saucepan, combine the rinsed rice, whole milk, water, and the cinnamon stick. Bring the mixture to a boil over medium-high heat, stirring occasionally.

Once boiling, reduce the heat to low, cover the saucepan partially (leaving a small gap for steam to escape), and simmer gently for about 30-40 minutes, or until the rice is tender and the liquid has thickened. Stir frequently to prevent sticking and scorching at the bottom.

Stir in the granulated sugar and salt. Continue to cook, uncovered, for another 10-15 minutes, stirring constantly, until the Arroz con Leche reaches your desired creamy consistency. It will thicken further as it cools.

Remove the saucepan from the heat. Discard the cinnamon stick. Stir in the vanilla extract.

Ladle the Arroz con Leche into individual serving bowls or a larger serving dish. Let it cool slightly before serving, or chill it completely in the refrigerator.