Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together peanut butter, butter, and sugars until smooth.
Add egg and vanilla extract, mixing until well combined.
In a separate bowl, whisk together flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until a soft dough forms.
Roll dough into small balls and place on the baking sheet.
Use a fork to press a crisscross pattern into each cookie.
Bake for 10-12 minutes, or until edges are lightly golden.
Allow cookies to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.