Preheat your oven to 375°F (190°C). Line two large baking sheets with parchment paper or silicone baking mats. Setting up your workspace beforehand ensures a smooth baking process.

In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Whisk for about 30 seconds to ensure the leavening agent (baking soda) and salt are evenly distributed throughout the flour. Set this bowl aside.

In the bowl of a stand mixer fitted with the paddle attachment, or using a large bowl and a hand mixer, beat the softened butter, creamy peanut butter, light brown sugar, and granulated sugar together. Beat on medium speed for 2 to 3 minutes until the mixture is light, fluffy, and well-combined. Scrape down the sides of the bowl frequently during this step to ensure uniform mixing.

Crack the large egg into the creamed mixture and add the vanilla extract. Beat again on medium speed until the egg is just incorporated. Be careful not to overmix at this stage.

Reduce the mixer speed to low. Gradually add the reserved flour mixture into the wet ingredients, mixing only until the flour streaks have mostly disappeared and a thick dough forms. Stop the mixer immediately once the dough comes together. Overmixing the flour will develop too much gluten, resulting in a tougher, less chewy cookie.

Use a standard cookie scoop (about 1.5 tablespoons) to scoop uniform balls of dough. Place the balls onto the prepared baking sheets. For chewier cookies that spread less, place the scooped dough balls in the refrigerator for 15 to 30 minutes before baking.

Before baking, use a fork to flatten each cookie dough ball slightly, pressing down in one direction, and then pressing again perpendicular to the first mark (creating the classic peanut butter cookie criss-cross pattern). This pattern helps the cookie flatten evenly and ensures thorough cooking.

Place the baking sheets into the preheated oven. Bake for 8 to 11 minutes. The cookies are done when the edges are set and lightly golden brown, but the centers still look slightly soft and puffy. Do not overbake, as they will become dry instead of chewy. If using two sheets, rotate them halfway through the baking time.

Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes. This crucial resting time allows the soft centers to finish setting up. After 5 minutes, carefully transfer the cookies to a wire rack to cool completely. Store airtight at room temperature.