Preheat oven to 350°F. Line two baking sheets with parchment paper.
Combine the flour, baking sod,a and salt in a medium bowl. Set aside.
In the bowl of a stand mixer, beat the peanut butter, butter and both sugars, until light and fluffy.
Add in the egg and vanilla, beating until incorporated.
Add the peanut pieces and stir to incorporate.
Gradually add in the flour mixture on low speed. Stir until dough forms.
Using a cookie scoop (about 1 heaping tablespoon of dough), drop rounded balls of dough onto prepared cookie sheet. Leaving space for spreading.
Bake for 10 to 14 minutes, or until edges are slightly browned, and remove from oven.
Let cool for 5 minutes on cookie sheets before transferring cookies to a wire rack to cool completely.
Store in an airtight container for up to 5 days.