Preheat your oven to 325 degrees F and line two large cookie sheets with parchment paper or silicone baking mats. Set aside.
In a large bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.
In your stand mixer, with paddle attachment fixed, cream together the butter, peanut butter, brown sugar and granulated sugar until smooth and creamy. Add each egg, one at a time, fully incorporating the first one before you add the second. Add the vanilla extract and mix again.
With the mixer set on low speed, gradually add the dry ingredients to the wet until the dough comes together. Fold in both chips until evenly distributed.
Roll the dough into 2 tablespoon-sized balls and place on the prepared cookie sheets. Bake for 12-13 minutes or until still soft in the center but starting to brown around the edges. Remove from heat and let cool for 3-4 minutes before transferring to a wire rack to cool the rest of the way.
Cookies will keep in an airtight container for 2-3 days.