In a medium saucepan, combine the milk, cooked rice, sugar, and salt. Heat over medium heat, stirring frequently, until the mixture begins to simmer.

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

In a small bowl, whisk together the egg yolks and vanilla extract. Gradually add a small amount of the hot rice mixture to the egg yolks, whisking constantly to temper the eggs.

Slowly pour the egg mixture back into the saucepan, stirring constantly. Cook for an additional 5 minutes until the pudding thickens.

Remove from heat and stir in cinnamon and butter if using. Let it cool slightly before serving.

Spoon the rice pudding into serving bowls. Top with raisins and chopped nuts if desired.

Serve warm or chilled, as preferred.