Steep instant espresso in boiling water and cool to room temperature. Mix with 4 egg yolks, and sugar and set in the top of a double boiler. Beat with an electric beater until mixture is thick and fluffy. Beating constantly, pour the rum into the egg yolk mixture in a slow thin stream and continue beating until mixture almost triples in volume; this may take 10 minutes or so.
To serve, spoon mixture into balloon wine glasses or goblets, or chill for 30 minutes and serve as a sauce over ladyfingers or angel food cake.