With an electric mixer on medium speed, beat the butter, sugar, and brown sugar until fluffy and lightened in color. Add the vanilla and egg, and mix until combined.
With the mixer on low speed, add the flour mixture to the butter mixture and mix just until combined or a few small streaks of flour remain. Stir in the peanuts, chocolate chunks, and salt.
Drop the dough by tablespoonfuls onto the prepared pan, leaving about 2 inches between the cookies. If you reserved any peanuts and chocolate for topping the cookies, add those to the tops of the cookies.