Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together the peanut butter, butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg and vanilla extract.
In another bowl, whisk together the flour, baking soda, and salt.
Gradually mix the dry ingredients into the wet ingredients until a soft dough forms.
Scoop tablespoon-sized portions of dough and roll into balls.
Place on the prepared baking sheet about 2 inches apart.
Use a fork to gently press a crisscross pattern on each cookie.
Bake for 10–12 minutes, or until the edges are lightly golden.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.