Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a bowl, whisk together the flour, baking soda, and salt; set this dry mixture aside.

In a separate large bowl, cream together the softened butter, granulated sugar, and brown sugar until the mixture is light and fluffy.

Beat in the egg, then stir in the creamy peanut butter and vanilla extract until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined and a soft dough forms.

Roll the dough into three evenly sized balls and place them on the prepared baking sheet, then flatten each ball slightly with a fork to create a crisscross pattern.

Bake the cookies in the preheated oven for 10-12 minutes, or until the edges are golden brown and the centers are set.

Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.