In bowl, beat whipping cream to stiff peaks form. In separate large bowl, beat mascarpone cheese with icing sugar until light and fluffy. Gently fold whipped cream into mascarpone mixture. Set aside.
Working with half the ladyfingers for the first layer, quickly dip each one into the coffee and lay side by side, in single layer, in 9 x 13-in. (3-L) baking dish (or lay unsoaked cookies into dish and brush on the coffee). Spread half the mascarpone mixture over top. Repeat the two layers once more. Finely grate chocolate overtop.
Cover and refrigerate at least 4 hr. or overnight.