Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or lightly grease them to prevent sticking.

In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Add the creamy peanut butter to the butter-sugar mixture and mix until well combined. Then, beat in the eggs one at a time, ensuring each egg is fully incorporated before adding the next. Stir in the vanilla extract.

In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, mixing just until combined. Avoid overmixing to keep the cookies tender.

Using a spatula or wooden spoon, fold in the rolled oats and chopped nuts (if using).

Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart. Flatten each ball slightly with a fork to create a crisscross pattern. Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown.

Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.