Preheat oven to 350 degrees F. Line an 8x8x2-inch baking pan with foil, extending foil over edges of pan; set aside.
In a medium bowl combine crushed cookies and melted butter. Press mixture into the bottom of prepared pan. Bake for 8 minutes. Cool slightly in pan on a wire rack.
Meanwhile, in a food processor combine powdered sugar and softened butter. Cover and process until butter is evenly distributed. With processor running, add milk and peppermint extract through feed tube until a paste forms. Spread peppermint mixture evenly over prepared crust. Freeze for 45 minutes.
In a medium microwave-safe bowl combine chopped chocolate and shortening. Microwave on 100 percent power (high) about 1 minute or until chocolate is melted, stirring once. Let chocolate cool for 15 minutes. Pour chocolate over peppermint layer, spreading evenly. Using the edges of the foil, lift uncut bars out of pan. Use a 1-1/2-inch round cookie cutter to cut into rounds* or use a sharp knife to cut into squares. Store in the freezer until serving time.
To help push the cookie cutter through the mixture, press the top of the cookie cutter with the bottom of a measuring cup.
Place peppermint bites in a single layer in an airtight container; cover. Store in the refrigerator for up to 2 weeks or freeze for up to 3 months.
For Aimee's version, top finished bites with crushed peppermint candies while chocolate is still wet.