Combine uncooked white rice, pitted cherries, and cinnamon sticks with enough water to cover everything completely. Let this mixture soak for at least 4 hours, or overnight.

Pour the soaked mixture into a high-powered blender and blend on high speed for about 2 to 3 minutes until creamy and smooth.

Strain the blended mixture using a fine mesh strainer placed over a large bowl, pressing the solids with a spatula to extract as much liquid as possible.

Pour the strained liquid back into a bowl or pitcher and incorporate the milk, sweetened condensed milk, and vanilla extract. Stir until well combined.

Refrigerate the horchata for at least 2 hours to chill thoroughly, stirring before serving.

Pour the horchata into tall glasses filled with ice. Garnish with a cinnamon stick or a few whole cherries if desired. Serve immediately.