Preheat your oven to 350°F (175°C).
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large mixing bowl, cream together the softened unsalted butter, light brown sugar, and white sugar until light and fluffy, about 2-3 minutes.
Add the creamy peanut butter, egg, and vanilla extract to the creamed mixture and mix until well combined.
Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined.
Using a cookie scoop or your hands, form the dough into balls about 1 inch in diameter. Roll in additional white sugar and place on a baking sheet lined with parchment paper.
Using a fork, press down on each cookie ball to create a crisscross pattern.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.
Remove from the oven and cool on the baking sheet for about 5 minutes before transferring to a wire rack.