Best-Ever Rice Pudding

In a large saucepan over medium heat, combine 5 cups milk, sugar, and salt. Bring to a boil, stirring occasionally. When milk is boiling, add rice and reduce to a simmer. Cook, stirring occasionally, until mixture is thick and rice is tender, 45 to 50 minutes. Remove from heat and stir in butter, vanilla, and remaining ½ cup milk. Serve hot or chill in refrigerator and serve cold, with a sprinkle of cinnamon.