Rinse the rice once, then put it in a bowl with the cinnamon and 3 cups of the water.
Cover and leave it at room temperature for at least 4 hours, or overnight in the fridge. The grains should swell and turn chalky white.
Tip the rice, cinnamon and all of the soaking water into a blender and blend on high for a full 2 minutes, until the mixture is a smooth, milky slurry with no grit you can feel between your fingers.
Add the remaining 2 cups of water and blend again briefly.
Strain through a fine mesh sieve lined with cheesecloth or a clean thin kitchen towel, pressing and squeezing to get the liquid through. Discard the solids.
Whisk in the whole milk, sweetened condensed milk and vanilla. Taste and adjust.
Chill thoroughly and serve over plenty of ice, stirring before each pour since it settles.