Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large mixing bowl, combine the creamy peanut butter, granulated sugar, and light brown sugar. Mix well until smooth and creamy.
Add the egg and vanilla extract to the peanut butter mixture and beat until fully incorporated.
In a small bowl, whisk together the baking soda and salt.
Add the dry ingredients to the wet ingredients and stir until just combined. Do not overmix.
Using a tablespoon or cookie scoop, scoop dough and roll into balls. Place the dough balls on the prepared baking sheets about 2 inches apart.
Use a fork to gently flatten each ball, creating a crisscross pattern on top.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are set but the centers still look slightly soft.
Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Store cooled cookies in an airtight container at room temperature for up to 5 days.