Line the bottom of a 10-inch/26 cm springform pan with parchment paper. In a food processor, pulse the cookies into fine crumbs. Add the melted butter and pulse until the mixture resembles wet sand. Press the crumbs firmly into the base and up the sides of the pan using the bottom of a measuring cup or glass. Chill while preparing the filling.

In a stand mixer fitted with the whisk attachment, combine the white cheese, cream cheese, heavy cream, sugar, pudding powder, and vanilla. Whip on medium-high speed until the mixture becomes thick, smooth, and holds stiff peaks, 3 to 4 minutes.

Spread half of the cream mixture evenly into the prepared crust. Quickly dip the ladyfingers, one at a time, into the cooled coffee and arrange in a single tight layer over the cream. Top with the remaining cream and smooth the surface with an offset spatula.

Cover and refrigerate for at least 3 hours or until fully set. Just before serving, carefully release the cheesecake from the pan and transfer to a serving plate. Dust the top generously with cocoa powder using a fine-mesh sieve.