Preheat your oven to 350°F (175°C). This ensures that the cookies bake evenly.
Line two baking sheets with parchment paper. This is crucial for preventing the cookies from sticking and makes for easy cleanup.
In a medium bowl, whisk together the unbleached all-purpose flour, baking soda, baking powder, and table salt. Set this mixture aside.
In a large mixing bowl, use an electric mixer to cream together the salted butter, crunchy peanut butter, granulated sugar, and dark brown sugar until the mixture is light and fluffy. This should take about 2-3 minutes.
Beat in the eggs one at a time, mixing well after each addition. Then, add the vanilla extract and mix until combined.
Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined. Be careful not to overmix, as this can lead to tougher cookies.
Gently fold in the roasted salted peanuts, ensuring they are evenly distributed throughout the dough.
Using a cookie scoop or spoon, portion out the dough onto your prepared baking sheets, leaving enough space between each cookie for spreading.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown and the centers look slightly underbaked. They will continue to firm up as they cool.
Allow the cookies to cool on the baking sheets for about 5 minutes before transferring them to a wire rack to cool completely. Enjoy your Chunky, Chewy Peanut Butter Cookies warm or at room temperature!