Preheat the 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 flour, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a handheld mixer, cream the butter, brown sugar, and granulated sugar together for 1 to 2 minutes or until well combined.
Mix in the peanut butter, egg, and vanilla extract until fully combined, making sure to stop and scrape down the sides of the bowl as needed.
Add the dry ingredients and mix until just combined.
Place the 3 tablespoons (40 grams) of granulated sugar in a small bowl. Using a 1.5 tablespoon cookie scoop, scoop the cookie dough, roll into a ball, and coat in the granulated sugar. Place each ball of cookie dough onto the prepared baking sheets, making sure to leave a little room between each one. Gently press each one down with a fork to make a small criss-cross pattern.
Bake for 10 to 12 minutes or until the tops of the cookies are set. Remove from the oven and allow to cool on the baking sheet for 5 to 10 minutes, then carefully transfer the cookies to a wire rack to cool completely.