In a mixing bowl set over but not touching a pan of simmering water, beat the egg yolks and sugar until the mixture is pale yellow and thick ribbons fall from the whisk (4 to 5 minutes). Transfer the mixture to the bowl of an electric mixer. Add the mascarpone cheese and beat until smooth and creamy (2 to 3 minutes). In a chilled large mixing bowl, beat the cream to stiff peaks. Add the rum, vanilla and the 2 tablespoons of espresso and beat until smooth. In a clean mixing bowl, beat the egg whites to stiff peaks (when the whisk is lifted straight out of the bowl and inverted, the whites should hold their shape). With a rubber spatula, gently fold the mascarpone mixture into the cream until blended and smooth. Add about 1 cup of the beaten egg whites and fold gently until blended. Add the remaining egg whites and fold gently until the mixture is smooth and blended. One at a time, submerge each ladyfinger into the remaining espresso, then place it on the bottom of a 6-quart glass or ceramic baking or serving dish (about 2 inches deep). Continue to form a complete layer. Spread half of the mascarpone mixture over the soaked ladyfingers until evenly covered. Arrange another layer of soaked ladyfingers over the mascarpone cream, then spread the remaining mascarpone cream evenly over the top. Dust the Tiramisù with cocoa powder to create a rich, dark topping. Refrigerate at least 4 hours or up to 1 day before serving.