Crush about 24 chocolate sandwich cookies into fine crumbs. You want a texture similar to wet sand. Mix the crumbs thoroughly with the melted butter.

Press the buttery cookie crumbs firmly into the bottom of a 9x13-inch baking dish. Use the bottom of a measuring cup to compress the crust evenly. Refrigerate for 15 minutes.

Beat the softened cream cheese, 1/2 cup powdered sugar, and vanilla extract until smooth and creamy. Scrape down the sides of the bowl to avoid lumps.

In a separate bowl, whip the cold heavy whipping cream with the remaining 1/2 cup powdered sugar until stiff peaks form. The cream should hold its shape when you lift the beaters.

Gently fold approximately half of the whipped cream into the cream cheese mixture. Use a rubber spatula and a light hand to keep the mixture airy.

Fold in 1 cup crushed chocolate sandwich cookies. Do not overmix or the cookies will turn the filling gray.

Spread the cookies-and-cream filling evenly over the chilled chocolate cookie crust.

Spread the remaining whipped cream evenly over the cookies-and-cream filling. An offset spatula works well here, but a regular spatula is fine.

Crush several additional cookies and sprinkle them generously over the whipped cream. Add chocolate chips if desired.

Cover and refrigerate for at least 6 hours, preferably overnight, until thoroughly chilled and firm.

Slice the chilled icebox cake into squares and serve cold.