Heat the apple cider in a large pot until hot (just how hot is up to you).
Put the butter, spices, salt, brown sugar, and vanilla extract in the bowl of a stand mixer or food processor. Beat or mix until combined. Note: you can also do this by hand, but that's definitely more annoying.
Add 2 tbsp of the butter compound to a heat-proof cup. Then add 4 tbsp of rum, and fill the rest of the cup with hot apple cider. Stir, and repeat with new cups until you've got the desired number of drinks. Add in any garnishes, and enjoy!