Bring 4 cups water to a boil. Add cinnamon sticks and let steep for 10 minutes.
Combine rice and almonds in a blender; blend to the consistency of sand. Transfer to a bowl and mix in cinnamon water. Cover and let sit for 6 hours.
Strain mixture through a fine-mesh sieve twice. Save cinnamon sticks but discard almond and rice solids. Add 6 cups cold water, sweetened condensed milk, and cinnamon sticks. Serve over ice.
