Preheat the oven to 350ºF. Line a 9x9" baking dish with parchment paper.
In a mixing bowl, combine the flour, baking soda, baking powder and salt. Stir until mixed well.
In another mixing bowl, combine softened butter, peanut butter, brown sugar and granulated sugar. Mix with an electric mixer until well blended.
Add the egg and vanilla extract and mix again until combined.
Slowly add flour mixture to butter mixture, mixing as you go until it's all just combined. Do not overmix.
Add chocolate chips and peanut butter chips and stir until combined.
Spread cookie batter into the pan. (optional: add a handful of chocolate and peanut butter chips to the top of the batter)
Cook for 20-22 minutes or until golden and cooked to your desired crispiness.
Once cool, remove from the baking dish and cut into 16 pieces.