Combine the uncooked long-grain rice with 4 cups of water in a large container fitted with a secure lid. Seal the container and refrigerate the mixture overnight, or for up to 2 days, allowing the rice to hydrate and release its flavor into the water.
Transfer the soaked rice and its water to a blender. Process the mixture until the rice has been finely pulverized.
Pour the blended mixture through a fine-mesh sieve into a spacious bowl or pitcher. Discard the remaining rice solids and retain the strained rice-infused liquid.
Add the evaporated milk, sweetened condensed milk, ground cinnamon, and vanilla extract to the strained rice water. Stir thoroughly until the dairy ingredients and flavorings are evenly incorporated.
Pour the prepared horchata into a saucepan and place it over medium heat. Warm it gently, stirring at regular intervals, until it reaches the desired serving temperature. Do not allow the mixture to boil.
Pour 6 ounces of warm horchata into a mug and add 2 ounces of freshly brewed espresso. Stir gently until the two components are fully combined.