Begin by melting the butter in a microwave or on the stovetop until completely liquefied. In a mixing bowl, combine the melted butter with the crushed ladyfingers and sugar. Mix until crumbs are evenly moistened. Press mixture into the bottom of a 9-inch springform pan. Chill for about 30 minutes to set.

In a large mixing bowl, beat the cream cheese with an electric mixer until smooth and creamy, about 2-3 minutes. Gradually add the cold brew coffee, sugar, and vanilla extract, blending well. Continue mixing until the filling is velvety and uniform.

Prepare a shallow dish with the cold brew coffee. Quickly dip each ladyfinger into the coffee, ensuring they are moistened but not soggy. Layer the soaked ladyfingers on top of the chilled crust.

Pour the cheesecake filling over the layer of soaked ladyfingers, ensuring even distribution. Spread the filling gently with a spatula.

Cover the springform pan with plastic wrap and refrigerate for at least 4 hours, ideally overnight.

Before serving, remove the cheesecake from the refrigerator and release the sides of the springform pan. Dust the top with cocoa powder.