In a bowl with a mixer beat mascarpone and sugar until smooth. Add cream and chocolate and beat until mixture holds stiff peaks. In a small bowl stir together coffee and rum and brush onto wafers.

Sandwich wafers together to form a tower using about two thirds cream mixture. On a plate arrange tower on its side and spread remaining cream over it. Chill cake, loosely covered, 30 minutes. With a sharp knife halve cake diagonally.