Rinse the rice five times to get rid of the extra starch.
In a stock pot, bring 2 cups of water to a boil. Turn the heat down to medium-high. Add the rice and cook, stirring every so often, until the water is almost absorbed.
Add 2 cups of hot milk, followed by the sugar, raisins and cinnamon stick.
Continue to stir constantly, so that the rice doesn't stick to the bottom of the pan. The pudding will be done when the rice is soft. Remove the pudding from the heat.
Add the butter, vanilla and salt. Stir to incorporate.
In a separate bowl, whisk the egg yolks with the remaining 2 tablespoons of milk. Add the egg mixture to the pudding and stir to incorporate.
Remove the cinnamon stick and serve warm or cool.
If the pudding is too thick, add a bit of extra milk until the desired consistency is achieved. To heat up the pudding the next day, add a splash of milk to loosen it up.