Add the rice and hot water to a blender. Quickly blend for about 30 seconds to roughly chop the rice. Add the cinnamon sticks and transfer the entire blender to the fridge for at least 2-3 hours.
When you're ready, blend the entire mixture again, including the cinnamon sticks, until smooth, about 30-60 seconds.
Strain the rice mixture through a triple layer of cheesecloth and a fine-meshed sieve. Use a spatula or spoon to push the liquid through.
Stir in the evaporated milk, condensed milk, cold water, and optional vanilla extract. Taste and add more sugar as needed. Chill until ready to serve, then pour into glasses with lots of crushed ice. Enjoy!
Note: There may be leftover rice grains that settle to the bottom of the horchata. Try not to stir those up, as they will give the horchata a gritty texture. I use a ladle to scoop out the horchata so as not to disturb them.