Combine evaporated milk, condensed milk, and coconut cream in a blender and puree until smooth.
Pour into a large pitcher or pot, and add the coffee, rum, and vanilla, and whisk well until evenly combined.
If desired, add 1-2 tablespoons of instant espresso powder and whisk in.
Transfer into bottles, add the cinnamon sticks, and chill in the refrigerator for at least 2 hours or until very cold.
Serve straight in small glasses or on the rocks in larger glasses, garnished with a bit of cinnamon if desired.
