Add rice to a fine-meshed strainer. Rinse under running warm water until the water runs clear, scrubbing the rice in between your fingers several times, about 30 seconds. Shake and lightly press with hands to drain.

To a high-speed blender, add the rice, cinnamon, almonds (if using), and 2 cups water. Blend on high speed until the ingredients are ground, about 1 minute. Add the remaining 2 cups of water and blend on high speed for 30 seconds. There should be some small pieces, and it should not be completely smooth.

Cover and transfer the blender cup to the refrigerator. Chill for at least 8 hours or overnight. Alternatively, transfer to a large bowl, cover, and refrigerate.

Pour the rice mixture through a fine mesh strainer lined with a triple layer of cheesecloth into a large bowl or pitcher. Form a pouch with the cheesecloth and gently squeeze out as much liquid as possible. Discard the cheesecloth and solids. For an even smoother consistency, strain again.

To the strained rice mixture, stir in the milk, sugar, and vanilla. Add more sweetener to taste.

Refrigerate before serving. Pour the horchata over ice, garnished with more ground cinnamon or a cinnamon stick.