Preheat your oven to 350 degrees F (180 degrees C) and place the oven rack in the center of the oven.
Prepare the baking sheet with parchment paper. You can either grease your baking sheets, spray them with cooking spray or use a silicone baking mat.
In a separate bowl whisk together the all-purpose flour, baking powder, and baking soda.
In a stand mixer or using hand mixer cream butter and sugar until well combined and fluffy. Scrape the sides of the bowl.
Add peanut butter and 1/4 tsp salt, and mix until all combined. Add 1 large egg at room temperature, and the vanilla. Beat all together until well combined.
Add dry flour mixture and beat on low speed. Scrape the sides then increase the speed and beat until all combined very well.
Roll dough into one-inch balls and place the cookies on the prepared baking sheet. Space them apart by about 10 cm.
Flat each ball with a fork in a criss-cross pattern. Bake cookies for 10-11 minutes or until the edges are lightly brown but the middle is still soft.
Allow cookies to cool completely on a baking sheet, they need to set before being transferred to a wire rack. They can be kept at room temperature for 3 to 5 days in an airtight container, or they can be frozen.