Separate the egg. Beat the white to stiff peaks; beat the yolk with the sugar and a pinch of allspice until pale.
Fold the two together to make a light batter.
Spoon a heaped tablespoon of batter into a warmed heatproof mug.
Add the aged rum and cognac and stir to loosen.
Top with hot milk, stirring as you pour, and finish with a heavy grating of fresh nutmeg.
Jerry Thomas claimed to have invented it; he almost certainly did not, but he wrote the definitive version in 1862 and it carried his name. The batter can be made ahead and kept refrigerated for a day, which is the only way to serve this to more than two people.
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