Prepare the Oven and Pan: Preheat the oven to 350°F (175°C). Lightly grease the inside of a 9-inch (23 cm) springform pan. Wrap the outside in two wide layers of heavy-duty aluminum foil, bringing the foil above the bottom seam to protect the pan from the water bath.

Make the Ladyfinger Crumbs: Place the crisp ladyfingers, granulated sugar, and espresso powder in a food processor. Process until the cookies form fine, even crumbs without large pieces.

Form the Crust: Add the melted butter and pulse until the crumbs are evenly moistened. Press the mixture firmly across the bottom of the springform pan. Use the flat bottom of a measuring cup to create an even, compact layer.

Bake the Crust: Bake for 9 to 10 minutes, until the crust smells lightly toasted and looks slightly darker around the edges. Place the pan on a wire rack while preparing the filling. Reduce the oven temperature to 325°F (165°C).

Dissolve the Espresso: Stir the espresso powder and hot water together in a small heatproof bowl until no dry granules remain. Set the mixture aside to cool slightly.

Smooth the Cream Cheese: Place the softened cream cheese in a large mixing bowl. Beat on medium-low speed for 1 to 2 minutes, until smooth and free of firm lumps. Scrape the bowl and beaters thoroughly.

Add the Mascarpone and Sugar: Add the room-temperature mascarpone and granulated sugar. Beat on low speed just until smooth and evenly combined. Do not whip at high speed, as excess air can cause the cheesecake to puff and crack.

Flavor the Filling: Add the dissolved espresso, sour cream, vanilla, and salt. Mix on low speed until the filling is uniformly tan and no white streaks remain. Scrape the bottom and sides of the bowl.

Add the Eggs Carefully: Add the eggs one at a time on low speed, mixing only until each egg disappears into the filling. Add the egg yolk last. Finish folding by hand with a flexible spatula. The batter should look smooth, glossy, and thick but pourable.

Fill the Pan: Pour the cheesecake batter over the warm or cooled crust. Smooth the top and tap the pan gently on the counter once or twice to release large air pockets.

Prepare the Water Bath: Place the wrapped springform pan inside a large roasting pan. Set the roasting pan on the center oven rack, then carefully pour hot water into the roasting pan until it reaches about 1 inch (2.5 cm) up the springform pan’s sides.

Bake the Cheesecake: Bake at 325°F (165°C) for 70 to 80 minutes. The outer 2 inches should look set and slightly puffed, while the center should move as one soft unit when the pan is gently nudged rather than rippling like liquid.

Check the Temperature: Insert an instant-read thermometer into the center without touching the crust. Egg dishes should reach 160°F (71°C) for food safety. Remove the cheesecake once it reaches that temperature and avoid prolonged baking, which can make the filling firm or grainy.

Cool Gradually in the Oven: Turn off the oven, prop the door open several inches, and leave the cheesecake inside for 1 hour. Gradual cooling reduces sudden contraction around the edges.

Cool at Room Temperature: Remove the cheesecake from the water bath and carefully discard the foil. Place the pan on a wire rack and cool for 1 hour. Run a thin knife around the upper edge if the filling appears attached to the pan.

Chill Thoroughly: Cover the pan without touching the surface and refrigerate the cheesecake for at least 6 hours, preferably overnight. The center must feel firm and completely cold before topping or slicing.

Make the Mascarpone Cream: Place the cold mascarpone, powdered sugar, and vanilla in a chilled mixing bowl. Beat on low speed for about 20 seconds. Slowly add the cold heavy cream, then increase to medium speed and whip until medium peaks form. The topping should hold its shape while remaining smooth and spreadable.

Top the Cheesecake: Remove the springform-pan collar: Spread the mascarpone cream evenly over the chilled cheesecake with an offset spatula, creating a smooth surface or shallow swirls.

Chill the Topping: Refrigerate the topped cheesecake for 30 minutes so the mascarpone cream can firm before slicing.

Finish and Serve: Sift the cocoa powder evenly over the mascarpone cream shortly before serving. Add shaved chocolate, if using. Cut the cheesecake into 12 slices with a thin, sharp knife, wiping the blade clean between cuts.