Preheat oven to 350°F (175°C) and line two large baking sheets with parchment paper.

In a stand mixer fitted with the paddle attachment, cream together 1 cup butter, granulated sugar, and brown sugar for 3 minutes until light and fluffy.

Add the egg and vanilla extract, beating until fully incorporated.

In a separate bowl, whisk together the flour, baking powder, and salt.

Gradually add the dry ingredients to the wet mixture on low speed until just combined.

Fold in 1 cup of the crushed chocolate sandwich cookies by hand.

Divide the dough into 12 equal portions (approximately 1/3 cup each), roll into balls, and place on prepared baking sheets.

Bake for 10-12 minutes until the edges are set; the centers should still look slightly underbaked.

Cool cookies on the pan for 10 minutes, then transfer to the refrigerator to chill for at least 30 minutes.

Prepare the frosting by beating the cream cheese and 1/2 cup butter until smooth.

Slowly add powdered sugar and heavy cream, whipping until a stiff but spreadable consistency is reached.

Fold the remaining 1/2 cup of finely crushed cookies into the frosting.

Pipe or spread the frosting onto the chilled cookies and top each with a mini chocolate sandwich cookie.

Serve chilled for the authentic milkshake experience.