Preheat oven to 350F. Line two baking sheets with parchment paper and set aside.
Place butter and sugars in the bowl of a large stand mixer, fitted with a paddle attachment OR in a large mixing bowl with a wooden spoon. Mix on medium speed or by hand until creamy, about 2 minutes. Add peanut butter, egg, and vanilla and mix until smooth.
In a small bowl, combine flour, baking soda, and salt. Mix flour mixture into peanut butter mixture until dough is just combined.
Wrap dough in plastic wrap and chill in refrigerator 2 hours or up to 6 days.
Remove dough from refrigerator and preheat oven to 350F. Scoop dough into 1 inch balls and place on prepared baking sheets. Roll dough balls in additional granulated sugar and space apart on sheet pan. Use a fork to make a criss-cross indention in each ball, flattening them slightly.
Bake cookies at 350F 10-12 minutes until edges of cookies are golden brown. Cool cookies on baking sheet 10 minutes before transferring to a wire cooling rack to cool completely.