Rinse 1 cup of uncooked long-grain white rice under cold running water until water runs clear. Place in a bowl with 4 cups of hot water and 2 Mexican cinnamon sticks; soak for at least 4 hours or overnight.

Drain rice and cinnamon sticks; discard soaking liquid. Blend soaked rice and cinnamon with 2 cups of fresh water in a high-speed blender until smooth and creamy, about 1-2 minutes.

Strain the mixture through a fine mesh sieve or cheesecloth over a large bowl, using a spatula to press for maximum liquid extraction.

Whisk in 2 cups of milk (or almond milk), 1 teaspoon of vanilla extract, and 1/2 cup of granulated sugar into the strained liquid. Adjust sweetness and add 1 teaspoon of ground cinnamon to taste.

Transfer horchata to a pitcher and refrigerate for at least 2 hours. Serve chilled over ice, stirring gently before serving. Optionally, garnish with a sprinkle of ground cinnamon or a cinnamon stick.