Combine the chocolate and milk in a heatproof bowl and place over a saucepan of simmering water. Heat, stirring often, until the chocolate melts. Remove from the heat and let cool slightly.
Whisk the egg yolks and sugar in a large bowl until thick and creamy. Whisk in the chocolate mixture.
Whip the cream in a bowl until stiff peaks form. Add the chocolate mixture and fold together just until combine. Using clean beaters, whip the egg whites until stiff peaks form. Stir some of the whites into the chocolate mixture, then fold in the rest.
Spoon into individual dishes. Cover and refrigerate at least 2 hours, until chilled. Garnish with grated chocolate and serve chilled.