In a large bowl, combine the rice, cinnamon stick, and water. Let it soak for at least 4 hours or overnight.
Blend the soaked rice, cinnamon, and soaking water until smooth.
Strain the mixture through a fine mesh strainer or cheesecloth into a pitcher, discarding the solids.
Stir in sugar, vanilla extract, and milk (if using). Adjust sweetness to taste.
Refrigerate until chilled, then serve over ice.
Notes
✔ For a dairy-free version, omit the milk.
✔ Add a pinch of nutmeg for extra flavor.
✔ Serve with a sprinkle of ground cinnamon on top for a decorative touch.