Preheat oven to 300F degrees.
With an electric hand mixer, beat butter just until creamy. Add sugar and beat on medium speed until mixture is light and fluffy, about 2 minutes.
Add flour and beat on medium speed JUST until crumbly.
Break apart or coarsely crumble the cookies and add to the cookie dough. Beat on medium-low just until cookies are incorporated. Over mixing will turn the dough from white to gray.
Press dough together on a lightly floured flat surface to form a ball. Roll dough out with a rolling pin or press down with hands or a smooth cylinder glass to 1/4-inch-thickness.
Cut out cookies with a round 2 inch cookie cutter and place on a parchment or foil-lined baking sheet about 1 inch apart.
Push together the dough scraps and reroll. Cut out the cookies and place on another baking sheet or wait for the first one to completely cool after baking.
Bake cookies for 21 minutes. They will not be lightly browned but rather pale. Let cool 1 minute on the baking sheet, then transfer to a wire cooling rack.
They will crisp up as they cool.
Store in an airtight container at room temperature or refrigerator. Freezes well.