Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, cream together the peanut butter, softened butter, granulated sugar, and brown sugar until smooth and creamy. Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the peanut butter mixture, mixing until well combined. Fold in the oats until evenly distributed throughout the dough.
Using a cookie scoop or spoon, drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Gently flatten each cookie with the back of a fork, creating a crisscross pattern.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.