Place egg yolks and sugar in the 5 quart mixer (small recipe). Beat eggs and sugar together on medium speed with flat beater until eggs and sugar are blended well and take on a pale color.
Add mascarpone and beat until smooth. Reduce speed of mixer and add rum and vanilla and blend until well mixed. In a separate bowl beat egg whites until stiff. Fold half of the egg whites into the mascarpone mixture.
Combine the espresso, Kahlua and in a mixing bowl.
Dip the lady fingers into the coffee mixture and line the bottom and sides of a 9 by 9-inch casserole. Place half of the mascarpone mixture over the lady fingers. Grate or chop the chocolate coarsely and add half of this over the first layer of the tiramisu. Repeat with the dipped lady fingers, the remainder of the mascarpone mixture, and the remainder of the chocolate to finish. Cover tightly with plastic wrap and refrigerate overnight.