In a large saucepan, bring the rice, water, and salt to a boil over medium-high heat. Reduce heat to low, cover, and simmer until the water is absorbed and the rice is tender, about 15-20 minutes.

Stir in the milk and sugar into the saucepan with the cooked rice. Cook uncovered over medium heat, stirring frequently, until the mixture thickens to a creamy consistency, approximately 15-20 minutes.

Remove from heat and mix in the vanilla extract. Serve the rice pudding warm in individual bowls, garnished with a sprinkle of ground cinnamon.