Rinse and drain the rice, then add it to a bowl with the hot water. Let the rice soak for several hours, or until softened.
Transfer the soaked rice and water to a blender. Blend until the rice is broken down and the mixture looks milky.
Strain the mixture through a fine-mesh sieve or cheesecloth, pressing out as much liquid as possible. Discard the rice solids.
Stir in the milk, sweetened condensed milk, vanilla extract, ube extract, and cinnamon. Taste and adjust the sweetness and ube flavor as desired.
Refrigerate until completely chilled.
Pour over ice and garnish with a sprinkle of ground cinnamon. Enjoy!