Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
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, vegetable oil, and vanilla extract to the peanut butter mixture. Stir until fully combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined and a dough forms.
Using a tablespoon or cookie scoop, scoop out dough and roll into balls. Place them about 2 inches apart on the prepared baking sheets.
Using a fork, gently press down on each dough ball to flatten slightly and create a crisscross pattern on top.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are lightly golden but the centers are still soft.
Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.