Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large bowl, mix peanut butter, butter, and both sugars until creamy.
Add the egg and vanilla extract, mixing well.
In another bowl, whisk together flour, baking soda, and salt.
Gradually mix the dry ingredients into the wet mixture until combined.
Scoop the dough onto the prepared baking sheet, pressing each ball slightly with a fork to create a criss-cross pattern.
Bake for 10-12 minutes or until edges are lightly golden.
Let cookies cool on the baking sheet for 5 minutes before transferring to a wire rack.