Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or lightly grease it.
In a mixing bowl, combine the peanut butter, brown sugar, and granulated sugar. Use an electric mixer or whisk to blend until smooth and creamy.
Add the egg and vanilla extract to the peanut butter mixture. Mix well until fully incorporated.
In a separate bowl, whisk together the baking soda, salt, and flour.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Using a cookie scoop or spoon, drop rounded tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Flatten each cookie 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. The centers may look slightly underbaked, but they will set as they cool.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.