Swedish Christmas Rice Pudding

In a heavy saucepan, combine the water, rice and salt; bring to a boil over medium heat. Reduce heat; cover and simmer for 15 minutes or until water is absorbed. Add milk and 1/3 cup sugar; bring to a boil. Reduce heat; simmer, uncovered, for 30-40 minutes or until slightly thickened. , Whisk together the eggs and remaining sugar. Gradually stir 2 cups hot rice mixture into the egg mixture; return all to pan, stirring constantly. Cook and stir over low heat for 3-5 minutes until mixture reaches 160°. Remove from the heat; stir in butter and vanilla. Pour into a serving bowl. , Refrigerate for 2 hours or until chilled. Just before serving, sprinkle with cinnamon.