Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone liners.
Whisk together the flour, baking powder, baking soda, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, sugar, brown sugar, and peanut butter until light and fluffy. Add the egg and vanilla, and mix well.
Gradually add the flour mixture, mixing just until combined or a few streaks of flour remain. Stir in the peanuts.
Drop the dough by 2-tablespoon portions onto the prepared pans. Use a fork to flatten the cookies and make a cross-hatch pattern on top of them. Bake, one pan at a time, 12-15 minutes, or until lightly browned.
Cool the cookies on the pan on a wire rack for 5 minutes. Then transfer the cookies to a wire rack to cool completely.
Notes
*Roasted, salted, unsalted, honey roasted... whatever kind of peanuts you like!
Store in an airtight container at room temperature up to 4 days.