Position an oven rack in the center of the oven and preheat to 350 degrees F. Line a 9-inch-square baking pan with foil, pressing it into the corners and up the sides, leaving an overhang on 2 sides. Spray with cooking spray. Set aside.
Place the butter in a small saucepan and melt over medium heat, about 3 minutes.
Meanwhile, whisk together the flour, baking powder and salt in a medium bowl and set aside.
Pour the melted butter into a large bowl and add the brown sugar and peanut butter. Whisk to combine, then add the eggs and vanilla and whisk until smooth.
Add the flour mixture and use a rubber spatula to mix just until a smooth batter forms. Add the peanut butter sandwich cookies and chocolate chips and stir until just combined. Transfer the batter to the prepared pan and spread out evenly using a small offset spatula or the bottom of a flat measuring cup, smoothing out the top. Sprinkle with 1 to 2 tablespoons additional chocolate chips.
Bake until the batter puffs and the edges are lightly browned, about 25 minutes, rotating the pan once halfway through the cooking time. Place the pan on a cooling rack and cool the blondies in the pan completely before lifting them out of the pan using the foil. Cut into 12 to 16 pieces and serve.