Preheat your oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats and set aside.
In a large mixing bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or using a handheld mixer), cream the softened butter, light brown sugar, and granulated sugar together on medium speed until light and fluffy (1–2 minutes).
Add the peanut butter, egg, and vanilla extract to the butter mixture. Beat until fully combined, scraping down the sides of the bowl as needed.
Gradually add the dry ingredients to the wet ingredients. Mix on low speed until just combined. Be careful not to overmix.
Optional: Place the granulated sugar in a small bowl. Scoop 1.5-tablespoon portions of cookie dough, roll into balls, and coat each in the granulated sugar.
Arrange the dough balls on the prepared baking sheets, leaving about 2 inches between each one. Use a fork to gently press each ball, creating a criss-cross pattern.
Bake the cookies for 10–12 minutes, or until the tops are set but not browned. The cookies will look slightly underbaked—this is key to keeping them soft!
Let the cookies cool on the baking sheet for 5–10 minutes, then transfer them to a wire rack to cool completely.
