In a large bowl, cream together the butter, granulated sugar, and brown sugar with an electric hand mixer.
Add the eggs, one at a time, and beat until incorporated. Add the vanilla and beat until combined.
Sift in the flour, cocoa powder, salt, and baking powder. Beat until combined.
Divide the dough into 4 equal portions. Place a portion of dough between 2 sheets of parchment paper and roll out into a circle that is about 11 inches (27 cm) wide. Using a 10-inch (25 cm) springform pan as your guide, cut a 10-inch (25 cm) circle out of the dough.
Use a 3-inch (8-cm) ramekin as a guide to cut out the center, leaving a doughnut-shaped cookie. Reserve the dough scraps and transfer the cookie on the parchment paper to a baking sheet. Repeat with the remaining dough portions.
Chill the cookie dough in the freezer for 10 minutes.
Bake the cookies (in batches, if necessary) for 12-14 minutes, until crisp around the edges. Let cool completely.
Reroll the dough scraps and use a cookie cutter to cut out 24 1½-inch-wide (4-cm) cookies. Transfer the cookies to a baking sheet lined with parchment paper and chill in the freezer for 10 minutes.
Bake the cookies for 7 minutes, until crisp. Let cool completely.
Make the whipped cream: Add the heavy cream to a large bowl. With an electric hand mixer, whip the cream until soft peaks form, then add the sweetened condensed milk. Continue whipping until stiff peaks form. Transfer to a piping bag or zip-top bag fitted with a large round tip.
Carefully place one of the large cookies on a serving platter. Pipe a layer of whipped cream on top of the cookie. Repeat with the remaining cookies and whipped cream, finishing with a layer of cream. Reserve any leftover whipped cream for sandwich cookie garnish.
Chill the cake in the refrigerator for at least 4 hours or overnight.
After the cake has chilled, make sandwich cookies for decoration. Pipe a dollop of whipped cream onto a small cookie and sandwich with another cookie. Make 9 more cookie sandwiches. Place the remaining cookies in a plastic bag and use a rolling pin to smash into crumbs.
Arrange the sandwich cookies evenly around the top edge of the cake. Sprinkle the cookie crumbs over the exposed whipped cream.
Slice and serve.
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