Steep the rice + cinnamon: In a bowl or jar, combine 1 cup of rice and 1 cinnamon stick with 2 cups of water. Let it sit at room temperature for at least 24 hours to soak. This is going to soften the rice and infuse that water with cinnamon flavor.
Blend + strain: The next day, blend the entire mixture (rice, cinnamon stick, and water) until smooth. Then strain it really well through a fine mesh strainer or cheesecloth. You want the liquid, not the pulp.
Cook the syrup base: Pour the strained rice “milk” into a small pot. Add 1 cup of sugar and ¾ cup of sweetened condensed milk. Bring it to a simmer over medium heat, stirring with a whisk the entire time. Rice has starch, so if you don’t stir it, it’ll clump up on you. It should thicken slightly—think the consistency of a syrup—after about 10 minutes.
Add the vanilla: Once thickened, remove from heat and stir in 1 tablespoon of vanilla paste. Give it a good whisk, then let it cool.
Store it: Once cooled, pour into a clean glass jar or bottle. Keep it in the fridge for up to 2 weeks!