Rinse the rice under running water until the water runs clear.
Add the rinsed rice, almonds, cinnamon stick, and 3 cups of water to a large bowl or pitcher. Cover and let it sit in the refrigerator for at least 8 hours, up to 24 hours.
Pour the bowl of ingredients into a large blender and add in the 3 cups of remaining water. Blend on high until completely smooth, about 2 to 5 minutes depending on the power of your blender. You may need to work in batches depending on the size of your blender.
Strain the blended mixture through a fine mesh strainer or nut milk bag to remove any solids. This may require straining 2 to 4 times to remove all the grittiness.
When completely smooth, pour it into a large pitcher and mix in the milk, evaporated milk, granulated sugar, and vanilla extract. Stir until all the ingredients are well combined.
Serve over ice and top with ground cinnamon.
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Notes
Ceylon cinnamon: Also referred to as "Mexican cinnamon." Ceylon cinnamon is light brown, fragile, and has a lot of layers that are easily broken, as opposed to Cassia cinnamon which is very hard and is not easily broken in half. Ceylon cinnamon can be easily found in Hispanic grocery stores or online. If you’re not using Mexican cinnamon, remove the cinnamon stick from the mixture before blending.
Separation of the water and the rice mixture is completely normal, especially if it's been sitting in the fridge for a day or two. Just mix it together with a large spoon and serve as you normally would.
To make it dairy-free, use a dairy milk alternative like almond, soy, coconut, oat, or cashew milk.
To make it nut-free, you can simply omit the almonds. No need to replace them.
To make this using sweetened condensed milk, replace the granulated sugar with 6-12 ounces of sweetened condensed milk for an extra creamy treat.