In a blender, combine the evaporated milk, cream of coconut, coconut milk, sweetened condensed milk, rum (if using), vanilla extract, and ground cinnamon. Blend on high speed for 1–2 minutes, or until the mixture is smooth and fully combined.

Pour the coconut mixture into glass bottles and seal tightly. Refrigerate until well chilled.

Before serving, stir or shake the bottle well to recombine the ingredients. Pour the coquito into small glasses and garnish with a sprinkle of ground cinnamon and a cinnamon stick, if desired.