Preheat the Oven - Set oven racks to the upper-middle and lower-middle positions. Preheat to 350°F (177°C). Line two baking sheets with parchment paper.
Mix Dry Ingredients - Whisk flour, salt, baking powder, and baking soda in a medium bowl.
Chop the Peanuts - Add peanuts to a food processor and pulse until fine crumbs are formed, about 14 pulses. Peanuts can also be finely chopped on a cutting board.
Cream the Butter - Using a stand mixer fitted with the paddle attachment or hand mixer, beat butter, brown sugar, and granulated sugar on medium speed until pale and fluffy, about 3 minutes.
Incorporate the Eggs - Add peanut butter and beat until combined, 30 seconds. Add vanilla and eggs one at a time until fully incorporated, scraping the bowl down as needed, about 30 seconds.
Add Dry Ingredients - Reduce mixer speed to low and slowly add flour mixture until combined, about 30 seconds. Add ground peanuts and mix until just incorporated.
Shape the Cookies - Roll dough into 3 tablespoon-sized balls, spacing them 2" apart on the sheet pan. Use a fork to press and make crosshatch marks on the top of the cookies.
Bake - Place the pan in the oven and bake until the edges are golden and the centers have puffed up but are beginning to deflate, 10 to 12 minutes. Switch and rotate baking sheet pans halfway through.Cool cookies for 10 minutes on the sheet pan, then transfer them to a wire rack and cool completely before serving.
Bake Time: The bottom tray may need 1 to 2 more minutes.
Make it Gluten-Free: Substitute gluten-free flour for all-purpose flour. I recommend Bob's Redmill 1:1 Gluten-Free Baking Flour.
Storing: Refrigerate raw dough for up to 1 week or freeze for 1 month. Store cookies in an airtight container for up to 1 week, or freeze for 3 months.
Recipe Adapted From: America's Test Kitchen, The Perfect Cookie.