Preheat oven to 325F/160C degrees. Line an 8×8-inch or 9×9-inch pan with parchment paper or foil, leaving enough overhang on the sides for lifting the bars out of the pan after baking. Grease the pan if you don't use foil.
In a medium bowl, sift together flour, baking powder, and salt. Set aside.
In a standing mixer fitted with the paddle attachment, beat together butter and peanut butter on medium speed until smooth. Add both sugars and beat until light and fluffy, about 2 minutes. Scrape down the sides and bottom of the bowl as necessary. Add the egg and vanilla and beat until combined. Add flour mixture and beat on low speed just until combined. Don’t over mix. Fold in chopped peanuts (reserve a few for the top if you like).
Scrape the dough into the prepared pan and smooth the top. Sprinkle with peanuts. Bake the bars for 20-25 minutes or until the top is golden brown and a toothpick inserted into the center comes out clean. Let the bars cool completely, then lift the bars out of the pan and cut into squares.
Store bars at room temperature or in the fridge in an airtight container for up to 3-4 days. Serve at room temperature. Bars can also be frozen for up to 2 months.