Cream butter for 1 minute on medium high. Stop and scrape down sides of bowl. Then add sugars; cream for at least 2 more more minutes, until light in color and fluffy. Scrape down sides a few times during mixing, as needed.
Add peanut butter and sourdough discard, and mix on medium for about 45 seconds, until the mixture is mostly homogenous. It doesn't have to be perfect. Add egg and vanilla, and mix on low for 45 seconds to combine, scraping down sides.
In a bowl, combine flour, baking powder, baking soda, salt. Whisk to combine.
Add dry mixture in two increments to the wet ingredients, with stand mixer on speed 2, low. Turn up speed to medium for 30ish seconds to fully combine, just until no flour streaks are left. Don't overmix. Refrigerate dough for 2 hours* (up to 24 hours) to allow dough to rest and absorb liquids.
When ready to bake, preheat oven to 375 degrees F. Scoop dough 55 gram dough balls. Roll in granulated sugar. Place 6 dough balls on a parchment lined baking sheet with room in between.
Bake for 9 minutes, then use pan-banging technique; lift one corner of the cookie sheet a few inches and let drop onto rack. Then do the same thing to one other corner. Let cookies bake for another 1 1/2 to 2 minutes (you'll see their centers will puff up), repeat the banging. Let cookies bake for another 1 to 2 minutes until they are set in the middle but slightly underbaked when you pull them out of oven to ensure chewiness. Remove cookies from oven and drop pan on counter once more, and let cool on pan 5 minutes before transfer to cooling rack.