Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper and set aside.
In a stand mixer with the paddle attachment, cream together the softened butter, light brown sugar, and granulated sugar on medium speed for about 3 minutes until light and fluffy.
Add the peanut butter to the mixture and mix for 1-2 minutes until smooth.
Add the egg and vanilla extract, mixing until combined and clump-free.
Add in the flour, salt, and baking soda. Mix until just combined, being careful not to overmix.
Scoop out the dough and portion it into 16 cookie dough balls. Roll each ball in sugar and place it onto the prepared baking sheet.
Using a fork, gently flatten each cookie, creating a crisscross pattern by turning the fork and pressing in the opposite direction.
Bake for 10 minutes, or until the cookies are lightly golden brown and firm on the edges.
Remove from the oven and let the cookies set on the baking sheet for 3-4 minutes before transferring them to a cooling rack to cool completely.