Preheat the oven to 350°F (175°C). Grease a 9x13 inch baking pan.

In a mixing bowl, cream together the softened butter, granulated sugar, brown sugar, and peanut butter until smooth.

Beat in the eggs one at a time, then stir in the vanilla extract.

In a separate bowl, whisk together the flour, baking soda, and salt.

Gradually add the dry ingredients to the wet mixture, mixing until just combined.

Spread the batter evenly into the prepared baking pan.

Bake in the preheated oven for 25 minutes, or until the edges are golden brown.

If using, sprinkle chocolate chips on top while the bars are still warm, allowing them to melt slightly.

Let the bars cool in the pan before cutting into squares.