Preheat your oven to 375°F (190°C) and line baking sheets with parchment paper.

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

Beat in the peanut butter, egg, and vanilla extract until all ingredients are well combined.

In a separate bowl, whisk together the flour, baking soda, and salt, then gradually add these dry ingredients to the wet mixture, mixing until just combined.

Roll the dough into 1-inch balls, place them 2 inches apart on the prepared baking sheets, and flatten each with a fork to create a crisscross pattern.

Bake the cookies for 8-10 minutes, or until their edges appear lightly golden, then let them cool on the baking sheets for a few minutes before transferring to a wire rack to cool completely.