In a blender, combine coconut milk, cream of coconut, sweetened condensed milk, evaporated milk, ground cinnamon, ground nutmeg, and vanilla extract.

Blend until smooth and creamy.

Add the white rum and blend briefly to incorporate.

Pour the mixture into bottles or jars and add a cinnamon stick if using.

Seal and refrigerate for at least 4 hours or overnight.

Shake well before serving and pour into small glasses. Garnish with a sprinkle of cinnamon or nutmeg.