Rinse the rice under cold water until the water runs mostly clear. Add the rinsed rice and cinnamon sticks to a large bowl or pitcher. Pour 4 cups of water over the rice and cinnamon. Cover and refrigerate for at least 8 hours or overnight.

Transfer the soaked rice, cinnamon sticks, and all soaking water to a blender. Add the ground cinnamon. Blend on high speed for 2 full minutes until the mixture is as smooth as possible.

Line a fine mesh strainer with cheesecloth and set it over a large pitcher. Pour the blended mixture through the strainer slowly, pressing the rice pulp with the back of a spoon to extract all liquid. Strain a second time for the smoothest texture.

Add the whole milk, sugar, vanilla extract, and 2 cups of cold water to the pitcher. Stir well for about 1 minute until the sugar is fully dissolved. Taste and adjust sweetness as desired.

Stir or shake well before serving. Pour over plenty of ice, dust the top with ground cinnamon, and garnish with a cinnamon stick.