In a large bowl combine the rice, hot water, condensed milk, heavy cream, and cinnamon sticks. Cover with plastic wrap and allow to sit until completely cooled to room temperature, about 1 hour.
Remove and discard cinnamon sticks. Transfer the rice, with a slotted spoon, to a blender or food processor. Reserve the liquid. Blend on high until completely smooth, about 3 minutes. Add the reserved milk liquid to the blender or food processor, with the puréed rice, and blend until completely combined, another 2 minutes.
Pour the blended mixture through a fine mesh sieve, into a large bowl or pitcher. Use a spoon to help you pass the liquid through the sieve. There should be a rice paste left over, toss that out. Pass the liquid a few times through the sieve, if you want a smooth popsicle.
Add the ground cinnamon and vanilla to the horchata and stir. Pour into a popsicle mold. Place the mold in the freezer for about 1 hour and then insert the wooden popsicle sticks. Return to the freezer and continue to freeze for another 3 to 4 hours, until they are completely frozen.
When ready to eat, run the bottom of the mold under warm water to help loosen the popsicles. Serve with a sprinkling of ground cinnamon. Enjoy!