Heat oven to 350°F. Line two baking sheets with parchment paper.
Whisk flour, baking soda, baking powder, and salt in a medium bowl.
Beat butter, peanut butter, brown sugar, and granulated sugar until creamy and fluffy, 2–3 minutes.
Mix in the beaten egg and vanilla until smooth, scraping the bowl as needed.
Add dry ingredients to the bowl and mix on low just until the dough comes together.
Fold in peanut butter chips and chopped peanuts until evenly distributed.
Scoop 1.5-tablespoon portions, roll into balls, and place 2 inches apart on sheets.
Flatten gently with a fork in a crisscross pattern. Chill 10 minutes for thicker cookies, if desired.
Bake 10–12 minutes until edges set and tops look dry. Cool 5 minutes, then move to a rack.