Position a rack in the lower third of the oven and preheat to 350 degrees . Wrap the outside of a 9-inch springform pan with foil and line the bottom with parchment paper.
Using a food processor, grind the ladyfingers into fine crumbs. Add the butter and espresso and pulse until incorporated. Transfer the mixture to the prepared pan and press to form a crust halfway up the side of the pan. Bake until set, 8 to 10 minutes; let cool. Lower the oven temperature to 325 degrees .
Meanwhile, using an electric mixer, beat the cream cheese on high speed until fluffy, about 2 minutes. Gradually beat in the sugar at high speed until smooth. Beat in the mascarpone, vanilla and salt. Add the eggs 1 at a time, beating well after each addition. Stir in 1/2 cup chocolate chips.
Set the springform pan in a roasting pan. Pour the mascarpone-chocolate chip mixture into the baked crust, then place the roasting pan in the oven. Pour enough boiling water into the roasting pan to reach halfway up the sides of the springform pan. Bake until the top is golden and the center is set but still jiggly, about 1 hour. Let cool in the water bath for 15 minutes, then transfer to a rack to cool completely. Refrigerate for 6 hours or up to 2 days. Remove the cheesecake from the springform pan. In a small, heatproof bowl, melt the remaining 1/4 cup chocolate chips in the microwave at low power, stirring until smooth. Transfer the chocolate to a resealable plastic bag. Snip a hole in the corner of the bag and drizzle the chocolate over the cake.