Add chocolate sandwich cookies to a large ziplock type bag and crush (with a rolling pin) until crumbs. Measure out crumbs, making sure to scrape the inside of the bag as needed to get all the bits. You do not need to remove the filling from the cookies.
Add 3/4 cup crumbs into a large bowl with flour, then add baking powder and salt and set aside.
In the bowl of an electric mixer, add butter (cold, but cut into pieces) and blend until butter is smooth.
Add sugar and blend until well combined and fluffy.
Add egg and vanilla and blend until fully incorporated.
With the mixer on low, slowly add the flour/crumb mixture.
Blend until all ingredients are combined and the dough begins to pull away from the sides of the bowl.
Remove dough and roll out on a lightly floured work surface, or roll out between two sheets of plastic wrap (and then no flour is needed).
Roll to dough to about 3/8" thick. Cutout desired shapes and place on a baking sheet lined with parchment paper or a Silpat type liner.
Chill entire baking sheet of cookies (in the fridge) while you heat the oven to 350°F.
Bake cookies for about 10 minutes, or until the top surface of the cookies not longer looks moist. Allow to cool a few minutes on the baking sheet, then move to a cooling rack. Cool completely before frosting.