Preheat your oven to 350°F (175°C).
Line two baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, add peanut butter, softened butter, granulated sugar and brown sugar. Mix until smooth and fluffy.
Beat in egg and vanilla extract until fully combined.
In a separate bowl, whisk together flour, baking soda and salt.
Gradually add dry ingredients to wet mixture, stirring just until a soft dough forms.
Scoop tablespoon-sized portions of dough and roll them into balls.
Place dough balls about 2 inches apart on the prepared baking sheets.
If desired, use a fork to gently press down each cookie, creating a crisscross pattern seen on many Peanut Butter Cookies.
Sprinkle a light dusting of granulated sugar over the tops.
Place in preheated oven and bake for 10 - 12 minutes, or until the edges are lightly golden. The centers may appear slightly soft but will firm up as the cookies cool.
Remove from oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Store in an airtight container for up to a week.