1Preheat oven to 350 degrees F (177 degrees C) and place rack in center of oven. Line two baking sheets with parchment paper.
2In the bowl of your electric mixer (or with a hand mixer), beat the butter and sugars until light and fluffy (about 2 - 3 minutes). Beat in the peanut butter. Add the egg and vanilla extract and beat to combine. In a separate bowl whisk together the flour, baking soda, and salt. Add to the peanut butter mixture and beat until incorporated. Fold in the chopped peanuts, if using. (If the batter is too soft to form into balls, place in the refrigerator for about an hour or until firm).
3Roll the batter into 1 inch (2.5 cm) balls. Transfer the cookies to the prepared baking sheet, placing about 2 inches (5 cm) apart. Then, using the tines of the fork that has been dipped in white granulated sugar, make a crisscross pattern.
4Bake the cookies for about 10 to 12 minutes, or until the cookies are lightly browned around the edges. Remove from oven and place on a wire rack to cool. Can be stored at room temperature, in an airtight container, for about a week. Freeze for longer storage.