Preheat your oven to 350°F (175°C) and line your baking sheets with parchment paper.
In a mixing bowl, combine the creamy peanut butter, granulated sugar, and brown sugar. Beat with an electric mixer or whisk until smooth and creamy.
Add the eggs one at a time, mixing well after each addition. Then, stir in the vanilla extract.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the peanut butter mixture, mixing until just combined. If using, fold in chocolate chips or chopped nuts at this stage.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 8-10 minutes or until the edges are lightly golden. The centers may look slightly underbaked, but they will set as they cool.
Remove from the oven and let cookies cool on the baking sheets for about 5 minutes, then transfer to a cooling rack to cool completely.