In a medium saucepan, combine the rice, milk, sugar, and salt.
Bring the mixture to a gentle simmer over medium heat, stirring occasionally.
Reduce the heat to low, cover, and cook for 30-40 minutes, stirring every 10 minutes to prevent sticking, until the rice is tender and the pudding has thickened.
Remove from heat. In a small bowl, whisk the egg yolks and vanilla extract.
Gradually whisk about 1 cup of the hot rice pudding mixture into the egg yolks to temper them. Then, stir the tempered egg yolk mixture back into the saucepan with the remaining rice pudding.
Cook over low heat, stirring constantly, for another 2-3 minutes, until slightly thickened. Do not boil.
Remove from heat and stir in the vanilla extract.
Serve warm or chilled. Sprinkle with cinnamon, if desired.
Notes
This old-fashioned rice pudding is best served warm or at room temperature. For a richer flavor, you can use heavy cream instead of some of the milk.