Put chocolate, coffee, and sugar in a large metal mixing bowl. Set bowl over a large pot filled with 1 in. simmering water. Melt chocolate, stirring often, until smooth. Remove from heat and set aside.
Whisk egg whites in a medium bowl with a mixer until they hold stiff peaks. Whisk cream in another bowl until soft ribbons form.
Stir yolks into warm chocolate mixture. Mix in liqueur. Using a rubber spatula, gently fold in whites until almost blended, then gently fold in whipped cream until no streaks remain.
Pour chocolate mixture into a large (8-cup) glass serving bowl. Cover bowl tightly with plastic wrap and chill until ready to serve. Serve with sweetened whipped cream.
Make ahead: Up to 3 days, covered and chilled.
Note: Nutritional analysis is per serving.