Rinse the rice in a colander under cold water. Add the rice, cinnamon sticks and 4 cups of water to a bowl. Cover and refrigerate overnight (best) or at least 4 hours.
1 cup uncooked long-grain white rice, 2 cinnamon sticks, broken into large pieces, 4 cups room temperature water
Take out most of the cinnamon sticks, leaving a few small pieces with the rice for extra flavor.
Add half of the rice and half of the soaking water to a blender, with some of the cinnamon pieces. Blend until very smooth, about 4 minutes. With a high-powered blender (Vitamix, Ninja), 1 to 2 minutes is plenty.
Pour through a fine-mesh strainer or cheesecloth into a large pitcher. Press on the solids with a spoon to get out as much liquid as possible.
Repeat with the rest of the rice, soaking water and cinnamon.
Stir in the evaporated milk, sweetened condensed milk, vanilla and 2 cups of the cold water. Taste, then add the remaining 2 cups for a lighter horchata, or leave it out for a thicker, creamier one.
1 can evaporated milk (12 oz / 354 ml each), 1 can sweetened condensed milk (12 to 14 oz / 354 to 397 g each), 4 cups cold water
Taste and add sugar if you'd like it sweeter.
Chill and stir well before serving over ice. It's normal for some rice to settle at the bottom, so just give it a stir!