How to Make It
Preheat the oven to 350° and position racks in the upper and lower thirds. In a medium bowl, whisk the flour with the salt, baking soda and baking powder. In a large bowl, using an electric mixer, beat the butter, peanut butter and both sugars at high speed until pale and fluffy, 2 minutes. Beat in the egg and vanilla. At low speed, gradually beat in the dry ingredients until just incorporated.
Form half of the dough into 1-inch balls and arrange them 2 inches apart on 2 large baking sheets. Using a fork, gently press the tops of the cookies to form a crosshatch pattern. Bake the cookies for 12 to 15 minutes, until lightly browned; shift the baking sheets from top to bottom and front to back halfway through baking. Let the cookies cool on the baking sheets for 2 minutes before transferring them to a rack to cool completely. Let the baking sheets cool slightly, then repeat with the remaining dough.