Whisk together yolks and mascarpone in a large bowl until smooth. Add granulated sugar; whisk until dissolved. Set aside.
Place biscotti in the bowl of a food processor; pulse to form coarse crumbs. Fold biscotti into mascarpone mixture; set aside.
In the bowl of an electric mixer fitted with the whisk attachment, add egg whites; beat until soft peaks form. Fold egg whites into mascarpone mixture; set aside.
Combine espresso and liqueur in a medium bowl; pour half the mixture into a pie plate. Quickly dip half the ladyfingers individually into the pie plate, and place in the bottom of a 13-by-9-inch glass baking dish; fit snugly to line. Evenly spread half the mascarpone mixture over ladyfingers; repeat layers.
In a large bowl, whisk together heavy cream, confectioners' sugar, and vanilla until soft peaks form. Spread whipped cream evenly over tiramisu; garnish with grated chocolate. Chill at least 2 hours and preferably overnight before serving.
Note: Raw eggs should not be used in food prepared for pregnant women, babies, young children, the elderly, or anyone whose health is compromised.