Preheat your oven to 350°F (175°C) and prepare two baking trays by lining them with parchment paper.
In a large mixing bowl, cream together the softened butter, peanut butter, brown sugar, and white sugar using a hand mixer or stand mixer until the mixture becomes pale and airy, about 2 to 3 minutes.
Incorporate the egg and vanilla extract into the creamed mixture, mixing until smooth and uniform.
Gradually add in the flour and baking soda, stirring only until the dry ingredients are absorbed and a soft dough forms. Avoid overworking the dough.
Using a tablespoon measure, portion out scoops of dough and roll them into balls. If desired, coat each ball lightly in additional granulated sugar. Arrange them on the prepared baking sheets, spaced evenly, and press gently with a fork to create a crosshatch design.
Place in the oven and bake for 9 to 11 minutes, or until the cookie edges appear firm while the centers remain slightly soft.
Allow the cookies to sit on the baking sheets for 5 minutes post-baking, then transfer them to a wire cooling rack to cool completely.