In a mixing bowl, combine butter and sugars until well mixed.
Add eggs and vanilla, and stir until combined.
Add flour, cocoa powder, cornstarch, baking powder, and salt and stir until combined.
Stir in the chopped peppermint bark.
Refrigerate dough balls for at least 30 minutes.
Preheat oven to 325° F. Line cookie sheet with parchment paper or a silicone baking mat. Place chilled dough balls approximately on lined cookie sheets. Using the palm of your hand, press down to flatten the balls to thick discs.
Bake for 12-15 minutes. Cool on the baking sheet for approximately 5 minutes, then transfer cookies to wire rack to cool completely.