Add the rice, 2 cups of the milk, salt, and the cinnamon stick to a heavy-bottomed saucepan. Bring the mixture just to a gentle simmer over medium heat.

Reduce the heat to low and cook uncovered for 20–25 minutes, stirring frequently to prevent sticking or scorching. Keep the mixture at a quiet simmer rather than a rolling boil.

Add the remaining 2 cups milk and the sugar. Continue cooking gently for 15–20 minutes, stirring often, until the rice is tender and the pudding is thick, creamy, and still loose enough to spoon.

Add the raisins during the last 5 minutes if desired. Remove the cinnamon stick, then stir in the vanilla extract and butter.

Let the pudding stand for 10–20 minutes before serving. Spoon it into bowls warm or chill it thoroughly, then finish with a light sprinkle of ground cinnamon.