Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In the bowl of an electric mixer, beat the butter, peanut butter, brown sugar, and vanilla on medium speed until well combined, about 1 minute.
Scrape down the sides of the bowl with a rubber spatula. Add the egg and beat until incorporated, about 20 seconds more.
Add the dry ingredients and mix on low speed until just combined, scraping the sides of the bowl as necessary.
Mix in the peanut butter chips and chopped peanuts.
Chill the dough for 1 hour (see note below).