Pre-heat oven to 350˚F.
Whisk the flour, salt, baking soda, and baking powder in a large bowl and set aside.
Beat butter and sugars in your stand mixer bowl combined with your paddle attachment. Mix on medium until light & fluffy (3-6 minutes). Beat in the peanut butter until fully combined (30 seconds). Beat in the vanilla, then the eggs (one at a time) and then scrape down the bowl.
Slowly add in flour mixture while beating together on low.
Take 3 tbs. and make dough balls with it. Place evenly on baking sheets (preferably on a Silpat) about 2 inches apart. Use a fork to make a criss-cross pattern on top by pressing it down on the dough balls.
Bake until golden and centers are puffed and beginning to deflate (10-12 minutes). Let it for 10 minutes then eat warm or transfer to wire rack and let them cool completely.
MAKE AHEAD:
The dough can be made up to 3 days in advance and stored in the fridge covered tightly. If freezing the dough, freeze in dough balls and then baking at 300 for 17-22 minutes (on the tray frozen). Frozen dough balls are good for up to one month.