Preheat oven to 350 degrees F. Line a 9x13-inch baking pan with foil, allowing excess foil to hang over pan edges. Grease foil.
Combine flour, baking powder, and salt in a small bowl; set aside.
In a separate large bowl, whisk the butter and brown sugar together until smooth. Add the eggs and vanilla and whisk until well incorporated. Whisk in the peanut butter until combined. Switch to a rubber spatula or wooden spoon, add the flour mixture and stir until just incorporated. Add the peanut butter chips and peanuts and mix until evenly distributed.
Scrape the batter into the prepared pan and smooth the top. Bake until a toothpick inserted into the center comes out with a few moist crumbs attached, 30 to 35 minutes, rotating the pan halfway through baking. Cool completely on a wire rack for at least 2 hours. Using the foil overhang, lift the blondies from the pan and transfer to a cutting board. Cut into squares. Store in an airtight container at room temperature.