Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper to prevent the cookies from sticking and make cleanup easier.
In a medium bowl, combine the all-purpose flour, rolled oats, baking soda, and salt. Stir well so the ingredients are evenly distributed. Set the bowl aside.
In a large mixing bowl, beat the softened butter, brown sugar, and granulated sugar until the mixture becomes creamy and fluffy. This usually takes about 2–3 minutes with an electric mixer.
Add the peanut butter and beat until smooth. Mix in the egg and vanilla extract until everything is fully combined. Scrape down the sides of the bowl if necessary.
Gradually add the dry ingredients to the peanut butter mixture. Stir until a thick cookie dough forms. If you are using chocolate chips, chopped peanuts, raisins, or cinnamon, fold them in now.
For thicker cookies with a better shape, refrigerate the dough for approximately 20 minutes. Chilling is optional, but it can help reduce spreading during baking.
Scoop about 1½ tablespoons of dough for each cookie and roll it into a ball. Place the balls on the prepared baking sheet, leaving approximately 2 inches between them. Flatten each ball slightly with your fingers or a fork.
Bake for 10–12 minutes, or until the edges are lightly golden and the centers look just set. Avoid overbaking because the cookies will continue to firm up as they cool.
Allow the cookies to rest on the baking sheet for 5 minutes before transferring them to a wire rack. Let them cool further, then serve with milk, tea, or coffee.