Rinse the rice under cold water until the water runs clear.

In a medium saucepan, combine the rinsed rice, coconut milk, whole milk, sugar, and salt.

Bring the mixture to a gentle boil over medium heat, then reduce the heat to low.

Simmer uncovered, stirring occasionally, until the rice is tender and the mixture has thickened to a pudding consistency, about 35-40 minutes.

Remove from heat and stir in the vanilla extract.

Pour the pudding into a serving dish or individual bowls.

Allow to cool slightly, then cover and refrigerate to chill thoroughly.

Serve chilled, garnished with a sprinkle of cinnamon if desired.