Line the base of a 9-inch springform pan with parchment and lightly grease the sides. Wrap the outside of the pan with two layers of heavy-duty foil to waterproof it. Heat the oven to 350°F (177°C).
For the crust, combine the crushed cookies with the melted butter until evenly moistened. Press firmly into the bottom and 1½ inches up the sides of the pan. Bake for 8 minutes, then set on a rack to cool 10 minutes. Reduce oven temperature to 300°F (150°C).
Bring a kettle of water to a boil for the water bath and place a large roasting pan on the middle oven rack.
Melt the chopped chocolate in a heatproof bowl set over a pot of barely simmering water (do not let the bowl touch the water), stirring until smooth. Remove from heat and let cool to lukewarm.
In a stand mixer fitted with the paddle, beat the cream cheese on low just until creamy, about 1 minute. Add sugar, cocoa powder, espresso powder, and salt; mix on low, scraping the bowl as needed, until perfectly smooth.
In a separate bowl, whisk together the sour cream, Baileys, and vanilla. Whisk a few spoonfuls of this mixture into the melted chocolate to loosen it (this prevents seizing), then whisk in the remaining sour cream mixture until glossy. With the mixer on low, stream the chocolate mixture into the cream cheese base and mix just until combined.
Lightly beat the eggs in a small bowl to break them up. Using a spatula, fold the eggs into the batter in two additions until no streaks remain; avoid whipping in excess air.
Pour the batter into the cooled crust. Tap the pan firmly on the counter a few times and run a skewer in a gentle swirl to pop surface bubbles.
Set the foil-wrapped pan inside the roasting pan in the oven. Carefully pour the hot water into the roasting pan to come about 1 inch up the sides of the springform. Bake at 300°F for 75–85 minutes, until the edges are set and the center still has a 2–3 inch wobble.
Turn off the oven and leave the cheesecake inside with the door closed for 30 minutes. Crack the door open and let it sit another 30 minutes. Transfer to a rack, run a thin knife around the edge to release, and cool 45–60 minutes more. Remove the foil, then cover and refrigerate at least 6 hours or overnight to fully set.
For the topping, chill a mixing bowl and beaters for 10 minutes. Whip the cream to soft peaks, then slowly add Baileys and superfine sugar and continue whipping to medium-stiff peaks. Unmold the cheesecake, remove the base parchment, and place on a serving plate. Spoon or pipe the Baileys whipped cream over the chilled cheesecake just before serving.