Mix butter and cookies until they form a paste. Line a springform pan bottom and side with foil; press cookie mixture onto bottom and side of pan.
Place water, 2/3 cup sweetened condensed milk and white chocolate in a microwave-safe bowl; microwave for 3 minutes at 15-second intervals or until the chocolate melts. Pour in the larger batch of dissolved gelatin and mix; mix in sugar completely. Separate ¼ part of the icing and add black food coloring to the rest; let cool to prevent curdling. Unmold the frozen cheesecake, place it on a rack and cover it with the black icing. Place the rest of the white icing in a bottle, draw 3 circles on the surface and with the help of a toothpick pull from the center to the outside to form the spider web.