Put 20 of the chocolate cookies (reserving 50 whole cookies) into a zippered plastic bag and, using a rolling pin, crush them to fine crumbs. Line an 8-inch round cake pan with enough plastic wrap to extend by 4 inches all around.
In a large bowl, using an electric mixer, beat the cream cheese at high speed until fluffy, about 3 minutes. Beat in the chocolate syrup and 1/4 cup of water and beat the chocolate cream for 2 minutes.
Arrange 9 cookies in an overlapping ring on the bottom of the prepared cake pan and place 1 cookie in the center. Spoon one-fourth of the chocolate cream (about 1 1/4 cups) over the cookies, being careful not to disturb them. Repeat with the remaining cookies and chocolate cream, ending with a layer of 10 cookies on top. Fold the plastic wrap over the top of the cake. Lightly tap the pan once or twice on a work surface. Refrigerate the cake for at least 8 hours and preferably overnight.
Peel back the plastic wrap and invert the cake onto a serving plate. Carefully peel off the plastic wrap. Press the cookie crumbs onto the side of the cake to coat evenly. Cut into wedges and serve.
Make ahead: The plastic-wrapped cake can be refrigerated for up to 3 days.
Total time: 30 minutes plus overnight chilling