Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper.
Whisk together flour, baking soda, and salt in a medium bowl. Set aside.
Beat softened butter, peanut butter, granulated sugar, and brown sugar in a large bowl with an electric mixer on medium speed for 2-3 minutes until light and fluffy.
Add egg and vanilla extract to the butter mixture and beat for 30 seconds until fully incorporated. Scrape down sides of bowl.
Add flour mixture to wet ingredients and mix on low speed just until no flour streaks remain. Do not overmix.
Scoop dough into 1½-tablespoon portions and roll into balls.
Roll each ball in granulated sugar to coat.
Place dough balls on prepared baking sheets, spacing them 2 inches apart.
Use a fork to press down gently in one direction, then rotate 90 degrees and press again to create a crisscross pattern.
Bake for 10-12 minutes until edges are set and lightly golden. Centers will look slightly underdone.
Let cookies cool on baking sheet for 5 minutes, then transfer to a wire rack to cool completely.