Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper. This prevents the cookies from sticking and promotes even baking.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt.
In a large mixing bowl, using a hand mixer on medium speed, cream together the softened unsalted butter, brown sugar, and granulated sugar until the mixture is light and fluffy, about 2 minutes.
Add the creamy peanut butter, room temperature egg, and vanilla extract to the creamed butter and sugar mixture. Mix until just combined, about 1 minute. Using a room temperature egg allows it to emulsify more effectively into the batter, resulting in a smoother dough.
Add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to over-mix, as this can develop the gluten in the flour, leading to tougher cookies.