Line a square 8x8" or 9x9" pan with foil, extending the sides of the foil over the edges of the pan. Mist lightly with cooking spray.
In a medium bowl, combine the brewed coffee and Kahlua. Dunk each ladyfinger, one at a time, into the coffee mixture and line the cookies up in the bottom of the pan - you should have 2 rows of ladyfingers with about 6 ladyfingers in each row. Break up any ladyfingers to fit if needed.
Meanwhile, beat the whipped cream cheese, confectioners' sugar, and vanilla together with an electric mixer until fluffy and combined, about 1 minute. Fold in the whipped cream or Cool Whip gently. Spread half of this mixture over the ladyfingers.
Repeat with dunking the remaining ladyfingers, lining them up, and spreading the remaining whipped cream mixture over top. Dust liberally with cocoa powder. Cover loosely and refrigerate until set, about 2-4 hours.