This old chestnut used to be enormously popular, and many homes had their own special Tom and Jerry bowls and mugs to bring out at Christmastime.
A Tom and Jerry bowl? Where does the bowl come in?
This is a complicated hot drink, requiring preparation and equipment, but it's worth it. You start by boiling a kettle of water and warming some glasses. Then you have to whip up some egg whites, and the yolks with sugar and spices, then you mix that part together in your Tom and Jerry bowl and put a spoonful into each warm glass, and then you can add the brandy and the rum (both), and finally the hot water and a sprinkle of nutmeg.
Well, that's a lot, but most of it is in mixing up the Tom and Jerry batter, which you can do ahead of time and have it ready and waiting in your Tom and Jerry bowl for when your guests arrive. You can see that this would be a lot of work to make a single drink, and no more work to mix it up for six people or a whole party.