Rinse the Rice: Place the long-grain white rice in a fine mesh strainer and rinse it under cold, running water until the water runs clear.
Blend the Rice: Transfer the rinsed rice into a blender. Pour in 2 cups of water and blend on high speed for 1 to 2 minutes until the rice is finely ground.
Strain the Mixture: Pour the blended rice mixture through a fine mesh sieve or cheesecloth into a large pitcher, pressing down to extract as much liquid as possible.
Combine Ingredients: In the pitcher with the strained rice liquid, add the remaining 2 cups of water, coconut milk, sweetened condensed milk, vanilla extract, and ground cinnamon. Stir until smooth.
Adjust the Flavor: Taste your horchata and stir in additional sweetened condensed milk or ground cinnamon if desired.
Chill the Horchata: Cover the pitcher and refrigerate for at least 2 hours.
Serve: Fill tall glasses with ice cubes and pour the chilled horchata over them. Top with toasted coconut flakes.
Notes
Chill the horchata for at least 2 hours for the best flavor.