Make the cupcakes: Preheat the oven to 350°F. Prepare two cupcake pans with about 22 liners (you may need more or less depending on amount of batter).
In a large mixing bowl or the bowl of a stand mixer fitted with a paddle attachment, whisk the flour, cocoa powder, sugar, crushed cookies, baking powder, baking soda, and salt. Add the mayo, water, and vanilla and beat with a hand or the stand mixer until just combined.
Place about 3 tbsp (45 ml) of batter into each cupcake liner. Bake in the preheated oven for 16-20 minutes, until a toothpick inserted into the center comes out clean or with just crumbs. Allow the cupcakes to cool completely.
Meanwhile, make the frosting: Place the butter into a large mixing bowl or the bowl of a stand mixer fitted with a paddle attachment. Beat for a few minutes, until light and fluffy. Add the powdered sugar, vanilla extract, and 1 tablespoon of milk and beat again, until light and fluffy. If necessary, mix in more milk, approximately 1/2 tablespoon at a time, until the desired consistency is reached. Scrape the sides as necessary. Finally, beat in the crushed cookies. To remove air bubbles, use a rubber scraper to stir the buttercream a bit and press it up against the sides of the bowl.
Frost and decorate the cupcakes: Place the frosting into a piping bag fitted with an open star tip. Frost a swirl on top of each cupcake. Place 1/2 of a cookie on top of each cupcake. Enjoy!