Finely grind ladyfingers, add melted butter, and mix well. Add 2 TB coffee and mix again.
Press into bottom of 9 inch springform pan and bake about 6-8 minutes (will bake quickly-keep an eye on it so it doesn't brown too much).
Cream together the cream cheese, mascarpone, and sugar until well blended.
Add the eggs, 1 at a time, and blend until just mixed. Add the coffee, blend lightly, then add flour and blend once more until smooth (but not too long).
Put remaining coffee into shallow bowl, dip whole ladyfingers and roll to coat, then shake out and place flat in bottom of prepared springform pan. Use whatever shape you want, breaking cookies in half to fit if necessary.
Pour cheesecake batter into the springform pan over the ladyfingers and smooth top.
Bake at 350F for about 40 minutes, or until center jiggles slightly.
Turn oven off, and crack door. Let cheesecake cool in oven for 20 minutes (or if it's the heat of the summer, remove cheesecake and let cool in microwave for 20 minutes so you don't completely heat up the house!).
Cool completely and chill, at least 4 hours or overnight. Cheesecakes taste better as they age. Sprinkle with cocoa powder or chocolate shavings before serving.