In a large mixing bowl, whisk together the all-purpose flour, baking soda, and salt. Set Aside.
Add the butter to bowl of a stand mixer and beat for 1 or 2 minutes until light and fluffy.
Add the brown and ½ cup white sugar into the bowl with the butter. Mix for another minute. Scrape down the sides if necessary.
Scoop the peanut butter into stand mixer and mix until combined.
Add the egg and vanilla extract to the dough and mix together.
Add the dry ingredients to the wet ingredients and mix together and fully combined.
Use a 2 inch cookie scoop to make cookie dough balls.
Roll the balls of cookie dough in the remaining ½ cup sugar and coat completely.
Place the cookie dough balls on a parchment lined baking sheet about 2 inches apart.
Use a fork to stamp a criss cross shape on each cookie.
Bake the cookies at 375 degrees for 10 minutes.
Allow the cookies to cool on the baking sheet for 5 minutes, then transfer to a cooling rack.