Whisk the egg yolks and sugar in the bowl of an electric mixer fitted with the whisk attachment on high speed for about 5 minutes, or until very thick and light yellow. Lower the speed to medium and add 1/4 cup rum, 1/4 cup espresso, and the mascarpone. Whisk until smooth.
Combine the remaining 1/4 cup rum and 1 1/4 cups espresso in a shallow bowl. Dip 1 side of each ladyfinger in the espresso/rum mixture and line the bottom of a 9 by 12 by 2-inch dish. Pour half the espresso cream mixture evenly on top. Dip 1 side of the remaining ladyfingers in the espresso/rum mixture and place them in a second layer in the dish. Pour the rest of the espresso cream over the top. Smooth the top and cover with plastic wrap. Refrigerate overnight.
You can find savoiardi and mascarpone in an Italian specialty store.