Combine the rice and cinnamon stick with 3 cups of warm water in a bowl. The water should feel comfortably warm to touch. Cover and let this mixture sit for at least 3 hours, though overnight soaking creates the silkiest results.

Remove the cinnamon stick and pour the entire mixture into a blender. Add the remaining 2 cups of water, whole milk, sweetened condensed milk, vanilla extract, and sugar. Blend on high speed for 60-90 seconds until the mixture appears completely smooth and frothy.

Pour the blended mixture through a fine-mesh strainer lined with cheesecloth or a clean kitchen towel into a pitcher. Press the solids gently with a spoon to extract maximum liquid. For ultra-smooth horchata, strain twice.

Refrigerate your horchata for at least 1 hour before serving. Stir well before pouring as mixture naturally separates. Serve over ice in tall glasses, and dust the top with ground cinnamon.