Preheat the oven to 350 F. Line 2 baking pans with parchment paper.
In a large mixing bowl, cream together the peanut butter, butter, sugar and brown sugar. Beat together until smooth & creamy best if using a stand mixer or hand mixer. Add the egg and vanilla extract and continue to mix until well combined.
In a small mixing bowl, whisk together the flour, baking soda, and salt. Stir in the flour mixture to the butter and sugar mixture and mix until well combined.
Use a cookie dough scoop, or spoon the dough into 1 inch balls. Roll in white granulated sugar if you desire and place onto baking sheet. Using a fork, press down on each ball of dough to flatten, creating a criss-cross pattern.
Bake for 8-9 minutes. Do not over bake. Let cool on the baking sheet for a few minutes and then transfer to a wire rack.