Blend the coquito. In a blender, combine the rum, nutmeg, cinnamon, vanilla, sweetened condensed milk, evaporated milk, and coconut milk. Blend for 1 minute or until smooth and creamy.
Chill overnight. Pour the mixture into a glass pitcher or container with a lid, add the cinnamon sticks, stir well and set in the fridge overnight. The coquito should be ready to serve the next day.
Enjoy! Mix well before serving and garnish with coconut whipped cream (optional) and a sprinkle of cinnamon.