Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, combine the peanut butter, granulated sugar, light brown sugar, and vegetable oil. Mix well until smooth and creamy.
Add the egg and vanilla extract to the peanut butter mixture and beat until fully incorporated.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Using a tablespoon or cookie scoop, scoop dough and roll into balls. Place them about 2 inches apart on the prepared baking sheets.
Flatten each cookie ball gently with a fork, making a crisscross pattern.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are set and lightly golden.
Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.