Crumble the chocolate and melt it with 3 tablespoons of cream in a hot water bath. In the meantime, separate the eggs. Beat the egg whites until stiff. Whisk egg yolk with rum and 1 pinch of salt. Whip remaining cream until stiff.
Stir the egg yolks into the melted chocolate until a creamy mass is formed. Fold in the beaten egg white and cream. Pour into glasses and chill for 1 hour. Peel oranges so that the white skin is completely removed.
Cut the fillets out of the parting skins and spread them on the cream. Caramelise the sugar in a pan until golden brown. Spoon "threads" over the jars. Serve immediately.