In a bowl, soak the rice in hot water with cinnamon sticks for at least 5 hours or overnight, until softened.
Blend until smooth, strain, and transfer to a bowl.
Add sweetened condensed milk, evaporated milk, and vanilla extract. Mix well.
To the blend, add cold water and fresh mango. Blend again until smooth and creamy.
Add it to the horchata base.
Chill in the fridge for at least 1 hour before serving.
Serve over ice and garnish with diced mango or a light sprinkle of cinnamon, if desired.