For the butter mixture: Add the butter, brown sugar, honey, cinnamon, cloves and allspice to a medium bowl. Using a rubber spatula, mix everything together until well combined. Transfer the mixture to a mason jar and screw on the lid. Refrigerate until ready to use.
For the cocktail: Add 2 tablespoons of the butter mixture to each coffee mug. Pour 2 ounces of rum into each mug. Top off with boiling water and stir to melt the butter. Garnish with any or all of the whipped cream, mini marshmallows, cinnamon sticks or star anise and serve.