In a medium saucepan, combine the cooked rice, coconut milk, brown sugar, and salt.
Place the saucepan over medium-low heat and cook, stirring frequently, until the mixture becomes thick and creamy, about 15-20 minutes.
Remove from the heat and stir in the vanilla extract.
Let the rice pudding cool for about 5 minutes before serving. It will continue to thicken as it cools.
Serve warm, or refrigerate for a few hours if you prefer a thicker, chilled rice pudding. Sprinkle with ground cinnamon before serving, if desired.
