Boil the espresso and add the rum. Let something get cold. Whip the cream until stiff, mix the mascarpone with the egg liqueur and fold in the cream.
Dip the ladyfingers briefly in the coffee and line the bottom of a baking dish with them. Spread the mascarpone cream on top, layer the soaked ladyfingers on top again, add the cream again, and so on until all the ingredients have been used up. Finish with the cream. Put in a cool place, preferably overnight.