Dip the first 18 ladyfingers in the espresso, and line the bottom of the 12 x 9 pan with them. Sprinkle half of the chopped chocolate, and add a generous dusting of the cocoa to the ladyfingers; set aside.
Combine the yolks and 3/4 cup of sugar and mix on high with a mixer about 10 minutes. By hand, mix in the mascarpone until incorporated and relatively lump-free; set aside.
With a mixer or by hand, whip the cream, 1/3 cup sugar and rum until stiff peaks are formed. Add the mascarpone mixture and whip again until homogeneous.
Spread half of the egg/cheese filling on the ladyfingers in the pan. Soak the remaining ladyfingers in espresso and make a second layer (with spaces in between the ladyfingers). Sprinkle with remaining filling evenly over the ladyfingers, and lightly sprinkle with more cocoa.
Wrap, refrigerate and chill 4 to 6 hours. Before serving, sprinkle again with a light dusting of cocoa. Slice and serve with a spoon or spatula.
