Melt butter in a large pot over medium heat. Blend in brown sugar and confectioners' sugar. Remove from heat, and whisk in the ice cream, cinnamon, and nutmeg. Pour mixture into a plastic container, seal, and freeze.
In a coffee mug, measure 1 tablespoon Hot Buttered Rum Batter and 1 fluid ounce of rum, then fill cup with boiling water. Stir, and sprinkle top of drink with nutmeg.