In a saucepan, combine the cooked rice, milk, sugar, cinnamon, and salt. Stir well to combine.

Heat the mixture over medium heat, stirring frequently until it begins to simmer.

Reduce the heat to low and cook for about 15 minutes, stirring occasionally.

In a separate bowl, beat the eggs and then temper them by adding a small amount of the hot rice mixture to the eggs, whisking constantly.

Slowly add the tempered egg mixture back into the saucepan, stirring continuously.

Cook for an additional 5-10 minutes until the pudding thickens to your desired consistency.

Remove from heat and stir in the vanilla extract. Let it cool slightly before serving.

Serve warm or chilled, topped with raisins, chopped nuts, and a sprinkle of cinnamon if desired.