In a medium bowl combine all ingredients. Beat with a mixer until smooth (you may have a few very small pieces of butter). Transfer to a freezer container and freeze until ready to use. Hot Buttered Rum base may be used right away or for up to 3 months.
To serve, place 1 to 2 tablespoons of the base and 1 to 2 tablespoons of amber or clear rum in a coffee mug and top with boiling water. Stir until base is dissolved. Sprinkle with additional nutmeg, if desired, and add a cinnamon stick. Makes about 35 servings.
For another hot beverage skip the rum and add hot brewed coffee instead of the water.