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Beat the egg yolks and sugar with an electric whisk until pale and thick, and the mixture leaves a thick trail on the surface when the beaters are lifted out.
Warm the milk and nutmeg in a pan over a low heat until simmering. Put the chocolate in a large heatproof bowl and pour over the hot milk mixture, stirring until completely melted and smooth.
Pour a little of the chocolate milk mixture into the beaten egg yolk mixture, whisking all the time. Add a third of the milk and whisk again, then repeat twice more until all the milk is incorporated.
Pour the eggnog into a pan and add the double cream. Cook over a low heat, stirring continuously until thickened slightly – it should coat the back of a spoon. Add the bourbon, chill until cold, then pour into glasses and top with grated nutmeg to serve.