Rinse the rice under cold running water for about 2 minutes until the water runs nearly clear. Drain well.

In a medium saucepan, combine the rinsed rice, coconut milk, sugar, cinnamon, and salt. Stir once, then place over medium heat. Cook until the mixture comes to a steady low boil, about 5 minutes, stirring once or twice.

Reduce the heat to low so the liquid is at a gentle simmer. Cover the pan leaving the lid slightly ajar, and cook for 20 to 25 minutes, stirring every 5 minutes. The rice should be tender and the pudding should look like a loose porridge that slowly fills in behind a spoon.

Turn off the heat and stir in the vanilla extract. Taste and add a pinch more salt if needed. Ladle into bowls, dust with extra cinnamon, and serve warm.