In a large heavy-bottomed saucepan, combine the rice with 3 cups of the milk, sugar, salt, and cinnamon stick. Bring to a gentle simmer over medium heat, stirring occasionally.

Lower the heat and simmer uncovered for about 30 to 35 minutes, stirring often to prevent sticking until the rice is very tender and mixture is creamy.

Stir in the raisins and simmer for an additional 5 minutes until they are plump and the pudding is thickened.

In a small bowl, whisk the egg yolks with the remaining 1 cup of milk until smooth. Temper the yolks by slowly adding about 1/2 cup of the hot rice mixture while whisking constantly.

Whisk the tempered egg mixture back into the saucepan. Cook over low heat, stirring constantly, for 3 to 4 minutes until thickened and coats the back of a spoon.

Remove from heat, discard the cinnamon stick, and stir in the butter, ground cinnamon, and vanilla until smooth.

Serve warm or chill with plastic wrap pressed onto the surface to prevent a skin from forming. If the pudding thickens too much in the refrigerator, loosen with a splash of warm milk before serving.

Finish with a dusting of cinnamon and a drizzle of cream if desired.