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

In a mixing bowl, whisk together the flour, baking soda, and salt.

In another bowl, use an electric mixer to cream together the peanut butter, softened butter, brown sugar, and granulated sugar until smooth.

Add the egg and vanilla extract to the creamed mixture and mix until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Scoop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake in the preheated oven for 8-10 minutes, or until the edges are lightly golden. The centers will look soft.

Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.