Preheat the oven to 350°F (175°C).

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

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

Gradually add the dry ingredients to the wet ingredients and mix until combined.

Drop tablespoon-sized balls of dough onto a baking sheet lined with parchment paper.

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

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

Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.