In a large saucepan, combine uncooked rice with coconut sugar and salt. Pour in the milk and vanilla extract, then give it a good stir and place over medium-high heat.
Cover the pot with a lid and bring the mixture to a boil. Once it reaches a boil, reduce the heat to low-medium, remove the lid. Add the cinnamon stick, if desired. Let it simmer uncovered for 25 to 35 minutes, stirring often to prevent sticking, until the rice is fully cooked and the pudding thickens.
Remove the cinnamon stick, if using it.
Scoop the rice pudding into individual ramekins or bowls and let it cool at room temperature for 30 minutes to 1 hour. The pudding will continue to thicken as it cools.
Serve with your favorite toppings, or cover the ramekins and refrigerate for up to 3 days. If desired, you can thin the pudding with a bit of milk before serving.