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 1 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 5 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 1/2 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.