Take the base out of a 9-in. round springform cake pan and lay a piece of plastic wrap on top of it. Cut around the base to trim excess. Replace base in springform pan and line with the plastic round. Coat sides of pan with cooking spray. Cut a 3x28 1/4-in. strip of parchment paper to line pan's sides.
Beat cream, confectioners' sugar, cocoa, 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.
Spread about 2 cups of the chocolate whipped-cream mixture in bottom of prepared pan. Top with a layer of cookies (all facing down), breaking them as needed to fill gaps. Repeat with whipped-cream mixture and cookies 4 additional times (for 5 layers total of each).
Spread top with remaining chocolate whipped-cream mixture. Wrap pan in plastic wrap. Refrigerate until set, at least 6 hours or up to 12 hours.
Unwrap pan. Remove sides of pan, and peel away parchment-paper strip. Place a platter on top of cake, and flip over to invert cake onto platter. Carefully remove bottom of pan and peel away plastic wrap. Decorate cake with nonpareil sprinkles. Cake may be lightly wrapped in plastic wrap and stored in refrigerator for up to 3 days.
Use a springform pan to replicate the classic party-cake shape.