Preheat oven to 375°F.
In a mixing bowl, cream together peanut butter, butter, and both sugars using an electric mixer on low speed until light and fluffy (about 3 minutes).
Add the egg and mix until just combined.
In a separate bowl, whisk together flour, baking soda, and salt. Gradually add this to the wet ingredients, mixing until fully incorporated.
Roll dough into 1-inch balls and place on a greased or parchment-lined baking sheet.
Flatten each ball with a fork, making a crisscross pattern.
Bake for 10 minutes, or until cookies are just beginning to turn golden.
Let cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.