Preheat the oven to 350°F (175°C).

In a mixing bowl, combine flour, baking soda, and salt. Set aside.

In another bowl, beat together peanut butter, granulated sugar, brown sugar, and vanilla extract until smooth.

Add the egg and mix until well combined.

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

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

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

Bake in the preheated oven for 8-10 minutes, or until the edges are lightly golden.

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