In a jar, combine the rice, cinnamon stick and 2 cups of the water. Put a lid on it and let it sit for 8 hours or overnight.
Pour the rice mixture, including the cinnamon stick, into a blender and blend for 15 to 20 seconds.
Add the remaining 2 cups of water and briefly blend again.
Line a strainer with cheesecloth and strain the rice mixture through it. You might have to stir it a bit to get it to strain through.
Add the simple syrup, vanilla and salt. Stir and chill. Serve over ice.
Notes
Simple syrup - mix ½ cup water and ½ cup sugar in a saucepan over medium high heat. Stir until the sugar has dissolved and remove from the heat. This will make a little more than you need for this recipe. Store in the fridge and use in other cocktails. This will keep for 5-7 days in the fridge. Note - the calorie count is inflated because it is taking into account all of the rice, when some of the rice is strained out. For a creamier version, use sweetened condensed milk instead of simple syrup.