Separate the yolks from the whites into two different mixing bowls. In the bowl with the yolks, add the sugar, and beat the yolk mixture with an electric mixer, until it reaches a creamy consistency. Add the mascarpone cream cheese and mix until thoroughly combined.
In the other mixing bowl, beat the egg whites until they turn into fluffy white peaks. Carefully fold the egg whites into the creamy yolk mixture.
In another bowl, mix together the espresso and vermouth. Dip the cookies in the coffee mixture for a few seconds, making sure they are wet outside but still somewhat dry in the middle. On the bottom of a 2 quart cake pan or casserole, arrange the dipped cookies in one tightly packed layer. Pour half of the mascarpone cream mixture on top of the cookies, and spread evenly. Add a second layer of soaked lady fingers, then evenly spread the remaining cream on top.
Coat the cake pan in plastic wrap, and leave the tiramisu to rest in the refrigerator for 3 to 4 hours. Sprinkle the tiramisu with chocolate shavings, just before serving.