In a large bowl, using an electric mixer with whisk attachment, beat egg yolks and sugar until thick and pale, about 5 minutes. Add mascarpone cheese and beat until smooth. Add one tablespoon of espresso and mix until thoroughly combined.
In a small shallow dish, add remaining espresso and rum. Dip each ladyfinger into espresso for only five seconds. Letting the ladyfingers soak too long will cause them to fall apart. Place the soaked ladyfinger on the bottom of a 13 by 9 inch baking dish, breaking them in half if necessary in order to fit the bottom.
Spread evenly half of the mascarpone mixture over the ladyfingers. Arrange another layer of soaked ladyfingers and top with remaining mascarpone mixture. Cover tiramisu with plastic wrap and refrigerate for at least 2 hours, up to 8 hours.