Preheat the oven to 350°F.
Line a cookie sheet with parchment paper or a silicone baking mat.
Place the granulated sugar in a small bowl and set aside.
In a medium mixing bowl, whisk together the all-purpose flour, baking soda, and kosher salt.
Set the dry ingredients aside.
In a separate large mixing bowl, use a stand mixer or electric hand mixer to cream the softened butter, light brown sugar, and creamy peanut butter until smooth and well combined.
Add the egg and pure vanilla extract.
Continue mixing until the ingredients are fully incorporated.
Gradually add the dry ingredients to the peanut butter mixture.
Mix just until combined. Do not overmix.
Divide the dough into portions of approximately 1 1/2 tbsp each.
Shape each portion of dough into a small log.
Roll each dough log in the prepared bowl of granulated sugar until lightly coated.
Arrange the dough logs on the prepared cookie sheet, spacing them approximately 2 inches apart.
Using the tines of a fork, press a criss-cross pattern into each dough log.
Gently pinch the center of each cookie to create a peanut shape.
Bake for 10 to 12 minutes, or until the edges are lightly browned and the centers remain soft.
Allow the cookies to cool on the baking sheet for 5 minutes.
Transfer the cookies to a wire rack and allow them to cool completely before filling.