Mix the instant coffee with the rum and half the grated dark chocolate. Melt the ice cream. Dip the biscotti in the coffee mixture and arrange them along the bottom and sides of a cake form.
Pour the melted ice cream on carefully and smooth it out. Make a second layer of biscotti. Put the tiramisu in the freezer to freeze for 2-3 hours. Before serving, whip the mascarpone with 3 tablespoons of sugar and the liqueur.
Cut the cake into pieces, cover with mascarpone and sprinkle with grated chocolate and the mocha coffee.