To Make the Batter:
Melt butter in a large pan over medium heat. Blend in brown sugar and confectioners' sugar. Remove from heat, and whisk in the ice cream, vanilla extract, cinnamon, and nutmeg.
Pour mixture into container(s), seal, and freeze.
Warm the mugs or glasses to be used by filling with hot water; then empty.
Rim the edge of the mug or glass with the cut orange and dip the rim in the combination of white and brown sugars.
Squeeze the juice from a quarter of the orange into the mug.
Fill the mug with the hot water and then add the rum and the batter.
Stir, top with a dollop of whipped cream (optional) and a sprinkle of nutmeg.