Chill a large mixing bowl and whisk attachment for 10 minutes. Line the bottom of a 9-inch springform pan with parchment; if you have acetate cake collar, line the sides for extra-smooth edges.
Set up a gentle double boiler: bring 1 inch of water to a bare simmer in a saucepan. In a heatproof bowl above the steam, combine the chopped chocolate, 1/3 cup of the heavy cream, and espresso powder. Stir until silky and fully melted, then remove from heat and let cool to lukewarm, about 10 minutes. Tip: If the mixture tightens, whisk in 1–2 teaspoons additional warm cream to smooth it out.
For the crust, mix the crushed cookies with the melted butter until all crumbs look damp and clump when pressed. Firmly pack into the bottom of the pan. Freeze for 10–12 minutes to set while you make the filling. Tip: If crumbs seem dry, drizzle in 1 more tablespoon melted butter.
Whip the remaining 1 2/3 cups cold heavy cream with the powdered sugar in the chilled bowl on medium-high speed to medium peaks—creamy and billowy, not rigid. Scoop about 1 cup of the whipped cream into a piping bag or bowl, cover, and refrigerate for topping; keep the rest chilled for folding into the filling.
In a separate large bowl, beat the cream cheese, granulated sugar, vanilla, and salt on medium speed until very smooth and fluffy, 2 minutes, scraping the bowl and paddle. Mix in half of the cooled chocolate mixture until combined, then blend in the rest. Stir in a big spoonful of whipped cream to lighten the batter.
Fold the remaining whipped cream (not the reserved topping) into the chocolate cream cheese in two additions, using broad, gentle strokes just until no streaks remain. Spread the filling into the chilled crust, smooth the top, and tap the pan a few times on the counter to release air bubbles.
Cover and refrigerate until fully set, at least 5 hours or overnight for the cleanest slices.
To finish, release the springform ring. Pipe or spoon the reserved whipped cream around the edges and shower with chocolate curls. For neat slices, warm a thin knife under hot water and wipe clean between cuts.