Whisk 4 egg yolks, 1 cup of icing sugar, and ½ teaspoon of vanilla extract until pale and creamy. Whisk in ½ cup of heavy cream, then slowly add ⅓ cup of rum.
Set the bowl over a pot of barely simmering water and whisk for about 10 minutes, until thick, taking it off the heat at 160°F / 71°C. Pour into small glasses or a sterilized bottle.