In the bowl of an electric mixer fitted with the whisk attachment, combine the heavy cream, mascarpone, Kahlua, vanilla, sugar, cocoa powder, and coffee. Mix on low speed to combine and then slowly raise the speed, until it forms firm peaks.
To assemble, place a small amount of cream in bottom of parfait glass, then break up cookies for second layer. Keep layering cream then cookies, ending with cream at the top of the glass.
Smooth the top, cover with plastic wrap. Can refrigerate overnight. When ready to serve, shave chocolate over the top.
If you heat the block of chocolate in a microwave for 30 seconds, you will get large shavings.