Rinse the Rice: Rinse it under cold water. This helps prevent clumping.
Heat the Milk: In a medium saucepan, bring the milk to a gentle simmer over medium heat. Add the cinnamon stick or ground cinnamon for an extra touch of flavor.
Cook the Rice: Stir in the rice and a pinch of salt. Reduce the heat to low, and let the rice simmer, uncovered, for about 20-30 minutes, stirring frequently to avoid sticking.
Add Sugar and Vanilla: Once the rice has softened and the mixture thickens, add the sugar and vanilla extract. Stir continuously until the sugar is dissolved, and the pudding reaches a creamy consistency.
Final Touches: Remove the saucepan from heat, and discard the cinnamon stick (if used). Let the pudding cool slightly before serving. Garnish with raisins, ground cinnamon, or a sprinkle of nutmeg if desired.