In bowl of electric mixer, cream yolks and sugar until smooth.
Add mascarpone and mix on low speed 2 minutes.
Fold in whipped cream; reserve.
In medium bowl, combine coffee, brandy and rum.
Dip 15 ladyfingers, one by one, into the espresso mixture and arrange in a single layer on a 10x15-inch platter (or 10x15-inch baking sheet covered with foil), forming a rectangle about 7x13 inches.
Cover with half the mascarpone-and-cream mixture.
Repeat layers with 15 more ladyfingers dipped in espresso mixture and remaining mascarpone-and-cream mixture.
Sift chocolate evenly over top.
Halve remaining ladyfingers; arrange vertically around edge of cake, cut-sides down.
Refrigerate at least 4 hours.
Cut into squares to serve.