Combine chocolate and rum in a small pot; nestle pot inside a larger pot filled with water and set aside to allow to melt.
Beat yolks in another small pot until pale and frothy.
Combine sugar and coffee in another pot; cook over medium heat until dissolved, 5-6 minutes. Pour coffee mixture into yolks in a stream, while whisking, set aside.
Pour water into a large pot to a depth of 2". Heat over medium-low heat until hot but not simmering. Nestle pot with yolk mixture over pot and cook, whisking vigorouslym until thick and creamy, about 8-9 minutes. Transfer yolk mixture to a clean bowl; beat with an electric mixer until cool; about 5 minutes.
Uncover chocolate mixture and stir; add butter and whisk until smooth. Fold chocolate-butter mixture into yolk mixture; set aside.
Beat egg whites in a bowl until just frothy. Add cream of tartar and salt; beat to stiff peaks. Stir 1/4 of the egg whites into chocolate-yolk mixture; gently fold in the rest. Spoon mousse into 6 serving cups or dishes. Chill until set. Beat cream to stiff peaks; transfer to a pastry bag with a star tip. Pipe a rosette of cream onto each mousse.