In a medium bowl, whisk the flour, baking powder, baking soda, and salt together, then set it aside.
Add the butter to a large bowl (either of a stand mixer with a paddle attachment or else a large mixing bowl and a hand mixer). Beat the butter on medium-high speed until smooth, about 1 minute. Add the granulated sugar and brown sugar and beat on medium-high speed until combined, about 2 minutes. Add the eggs, peanut butter, and vanilla and beat on high speed until combined, about 1 minute. Scrape down the sides and up the bottom of the bowl and beat again as needed to combine.
Add the dry ingredients to the wet ingredients and mix on low until combined. With the mixer running on low speed, add the oats. Once combined, beat in the chocolate chips. The dough will be a little sticky and that’s just fine. Cover and chill the dough for at least 20 minutes in the refrigerator (and up to 4 days). If you keep it in the fridge longer than 20 minutes, allow it to get to room temperature before baking.
Preheat oven to 350°F.
Scoop balls of dough, 2 Tablespoons of dough per cookie, and arrange on the baking sheets. Bake for 12-14 minutes until lightly browned on the sides. The centers will look very soft.
Remove from the oven and allow to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely. Enjoy!