Preheat the oven: Preheat the oven to 350°F. Line two baking sheets with parchment paper or silicone baking mats.
Mix the dry ingredients: In a medium bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.
1 ⅓ cup all-purpose flour, 1 tsp baking soda, ½ tsp baking powder, ½ tsp salt
Cream the butter and sugars: In the bowl of a stand mixer fitted with the paddle attachment, or using a large bowl and hand mixer, beat the softened butter, brown sugar, and granulated sugar until light and creamy, about 2 minutes.
½ cup unsalted butter, ¾ cup light brown sugar, ½ cup granulated sugar, 1 cup creamy peanut butter
Add the wet ingredients: Beat in the vanilla and egg just until combined, about 20 seconds. Add the peanut butter and mix until smooth, about 20 seconds more.
1 tsp vanilla, 1 large egg
Finish the dough: Gradually add the flour mixture and mix just until no streaks of flour remain. Avoid overmixing.
Scoop the cookies: Using a medium cookie scoop, portion the dough onto the prepared baking sheets, spacing the cookies about 2 inches apart. If desired, sprinkle the tops lightly with additional granulated sugar.
Bake: Bake for 9–11 minutes, or until the tops look dry and the cookies are set but the edges have not yet browned. Don't overbake. Let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.