The cookies can be stored in an airtight container for up to 3 days.
Cream the butter, brown sugar and sugar together until fluffy. Beat in the peanut butter, followed by the egg and vanilla.
In a separate bowl, stir the flour, cornstarch, baking soda and salt. Add the flour mixture into the butter mixture and stir until evenly blended.
Drop tablespoonfuls of the cookies dough onto the prepared baking trays leaving 1 1/2 inches between the cookies. Using a fork dipped in flour, make crisscrosses on the top of each cookie, pressing the cookie down at the same time. Bake the cookies for 12 to 14 minutes until they are lightly browned. Let the cookies cool for 5 minutes before removing from the tray to cool completely.