In a medium saucepan, bring 1 1/2 cups of water to a boil. Stir in the rice, and reduce the heat to low.
Cover and simmer for 20 minutes until the rice is tender.
In another saucepan, combine cooked rice, milk, sugar, and salt. Cook over medium heat until thick and creamy for about 15 to 20 minutes. Stir frequently.
Remove from heat, and stir in the vanilla extract and butter.
Transfer to serving dishes and sprinkle with cinnamon before serving.