Make the coffee and pour it into a shallow bowl wide enough for soaking the ladyfingers. Set aside to cool.
Soak half the ladyfingers in the coffee, 2 at a time, allowing the liquid to penetrate them completely but letting the excess drain out of them,and place them in a single layer on bottom of a 3-quart serving dish at least 11/2 inches deep.
Whisk the egg yolks and sugar with an electric mixer, or by hand with a whisk, until smooth and pale yellow and mixture forms ribbons, 2-3minutes. Mix in the Strega and rum, then mix in the mascarpone, about 1/2 cup at a time,being careful not to over whip the mixture so it does not separate.
In a separate bowl whip the cream until it forms firm peaks. Carefully fold into the mascarpone mixture with a rubber spatula. Spread half of the mascarpone mixture over the coffee soaked ladyfingers. Soak the remaining ladyfingers and arrange them over the mascarpone, then spread the remaining mascarpone mixture on top. Use a fine mesh strainer or sifter to sprinkle the cocoa over the top, covering the mascarpone mixture completely. Cover the dish with plastic wrap and refrigerate for 12 hours, or overnight.
Serve chilled, cutting the Tiramisú into square portions with a serving spatula and placing them on dessert plates.