In bowl, combine heavy cream, mascarpone, sugar, Kahlua, cocoa powder, instant coffee, and vanilla. Mix on low speed with wisk attachments to combine and then slowly raise the speed, until it forms firm peaks.
To assemble cake, arrange cookies flat in an 8-inch springform pan, covering the bottom as much as possible. (break cookies to fill in spaces.) Spread a fifth of the whipped cream evenly over the cookies. Place another layer of cookies on top, lying flat and touching, followed by another fifth of the cream. Continue layering cookies and cream until there are 5 layers of each, ending with a layer of cream. Smooth the top, cover with Saran wrap, and refrigerate overnight.
Run a sharp knife around the outside of the cake and remove the sides of the pan. Shave chocolate over the top of the cake, and serve cold.