Beat cream, confectioners' sugar, and vanilla in the bowl of a stand mixer fitted with a whisk attachment on medium speed until starting to thicken, about 1 minute. Raise mixer speed to medium-high; beat until medium-to-stiff peaks form, 3 to 4 minutes.
Line a 6-cup glass bowl with 2 long, overlapping pieces of plastic wrap. Place 1 cookie in the bottom of the bowl. Press 6 cookies onto plastic wrap in a circle around bottom cookie, leaving about 1/2 in. between bottom cookie and cookie circle.
Using the back of a spoon or a small offset spatula, spread about 1 cup whipped-cream mixture into the bottom of the bowl (the cream will secure the cookie circle in the bowl); smooth top. Top with a single layer of cookies to make a horizontal "cake layer," breaking cookies as needed to fill any gaps and create a solid layer. Repeat layering process with whipped-cream mixture and cookies until you are about 2 in. from the top of the bowl.
Break 4 cookies in half, and press the 8 halves onto plastic wrap around the upper edge of the bowl, about 1 in. apart, placing broken cookie sides flush with the bowl's rim; cookies should be standing up vertically.
Resume layering with the whipped-cream mixture and the unbroken cookies until you reach the top of the bowl; finish with a layer of whipped-cream mixture.
Fold plastic wrap overhang over cake to cover. Refrigerate until cake is set and cookies have softened, at least 6 hours or up to 12 hours.
Remove plastic wrap on cake. Place a platter over cake, and flip bowl over to invert cake onto platter. Remove bowl; carefully peel off plastic wrap from cake. Smooth any wrinkles in whipped cream with the back of a spoon, making sure not to get any on the cookies. Cake may be lightly wrapped in plastic and stored in refrigerator for up to 3 days.