Combine the rice, coconut milk, 2 cups of the almond milk, sugar, and salt in a medium saucepan and bring to a gentle simmer over medium heat.
Reduce the heat to low and simmer uncovered for 25 to 30 minutes, stirring often so nothing sticks, until the rice is tender and the mixture is thick and creamy.
Stir in the remaining 1/2 cup almond milk, the vanilla, and the cinnamon, and cook for 2 more minutes. The pudding should be loose and spoonable since it thickens as it cools.
Remove from the heat and let it rest for 10 minutes.
Serve warm with an extra dusting of cinnamon, or chill for a few hours for a cold, extra thick pudding.