In a blender, combine the Coco Licor, white rum, coconut milk, sweetened condensed milk, vanilla extract, ground cinnamon, and nutmeg. Blend until smooth and creamy.
Pour the mixture into a glass bottle and refrigerate for at least 2 hours or overnight for best results.
When you're ready to serve, give the bottle a gentle shake and pour the Coquito into glasses filled with ice.
Garnish with a sprinkle of ground cinnamon and a cinnamon stick for that extra touch of island charm.