Make the crust: Line a 9-by-13-inch baking dish with foil, leaving an overhang. Put the butter and chocolate in a microwave-safe bowl; microwave in 30-second intervals, stirring, until melted and smooth. Pulse the cookies with the sugar in a food processor until finely ground. With the motor running, pour in the warm melted chocolate mixture and process until combined. Press the crumb mixture into the bottom of the prepared pan and refrigerate while you make the filling.
Make the filling: Warm the lime juice in a small saucepan over low heat; whisk in the gelatin and sugar until completely dissolved, then remove from the heat and let cool slightly. Beat the cream cheese in a large bowl with a mixer on high speed until smooth and fluffy, about 4 minutes. Add the sweetened condensed milk and beat until smooth. Beat in the gelatin mixture and vanilla. Spread in the prepared crust and refrigerate until firm, at least 4 hours or overnight. Melt the chocolate in a microwave-safe bowl in 30-second intervals, stirring, until smooth. Drizzle over the cheesecake and refrigerate until ready to serve. Remove from the pan using the foil handles and slice into bars. Photograph by Johnny Miller