Using a hand mixture or stand mixer with a paddle attachment, combine the softened butter, white sugar, and brown sugar together in a large mixing bowl. Cream together on medium-high speed for about 2 minutes.
Add peanut butter, sourdough discard, eggs, and vanilla extract to the bowl. Mix to combine, stopping occasionally to scrape down the sides of the bowl with a spatula.
Add salt, baking powder, baking soda, and ½ cup of the flour. Mix to combine. Add the remaining 1 cup of flour and scrape down the sides of the bowl with a spatula to make sure everything is evenly combined.
Add quick oats ½ cup at a time while the mixer is running on low speed. Continue until all the oats have been added. The batter will be very thick so stop the mixer halfway through to scrape down the sides and the bottom of the bowl.
Add chocolate chips or chocolate chunks and mix on low speed. Use a spatula to fully mix the bottom. Again, the batter will be THICK.
Cover the bowl with plastic wrap and chill in the refrigerator for up to an hour. You want the dough firm enough to be scooped into round balls but not too hard that it's unable to be easily scooped.
Once dough has chilled, preheat oven to 350℉ (177℃). Line a large baking sheet with parchment paper.
Using a large spoon, ice cream scoop, or cookie scoop, scoop balls of dough and place spaced apart on baking sheet. You can dot the tops of the cookie dough balls with a few more chocolate chips for looks before baking.
Bake for 12-14 minutes until the edges are golden and the center still looks a bit underdone. Do not over bake! Remove the pan from the oven and allow cookies to rest on the pan for 5 minutes before transferring to a wire cooling rack.
In between baking trays of cookies, put the dough back in the fridge so it stays chilled and easy to scoop. Allow the baked cookies to cool on a wire rack and then enjoy!