For the buttered rum batter:
Add the softened butter to a large mixing bowl along with both sugars, plus the cinnamon, cloves, and nutmeg. Beat on medium speed until well combined, about 1 to 2 minutes.
Add the softened ice cream and stir in on medium speed until fairly smooth, about 1 minute. The batter will be in a somewhat liquid state but will firm up when chilled.
At this point you can store the batter in a freezer-safe container and freeze until you’re ready to mix up your cocktails.
Makes about 2-½ cups hot buttered rum batter, enough for 10 to 12 cocktails.
For each hot buttered rum:
Scoop the buttered rum batter into a mug.
Pour the rum in followed by the boiling water, stirring well to blend.