In a saucepan, combine the milk, sugar, and vanilla.Heat, stirring constantly.
After 5 minutes, add the rice and reduce the heat.Continue cooking, stirring frequently, for about 30 to 40 minutes, until the milk just covers the rice and the mixture is creamy.
Remove from heat, add the butter (optional), and mix well.
Divide the rice pudding among individual ramekins and let cool to room temperature for 1 hour.Enjoy the same day or store in the refrigerator.