Preheat the oven to 350°F (175°C).

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

In another bowl, combine the peanut butter, brown sugar, granulated sugar, egg, and vanilla extract. Mix until smooth.

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

Scoop tablespoon-sized balls of dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart.

Flatten each ball slightly with a fork, creating a crisscross pattern on top.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.

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