In a medium bowl, sift together the all-purpose flour, cornstarch, salt, and baking powder.
Slowly introduce the dry ingredients into the wet mixture in three stages, mixing on low speed until combined. Remember to scrape down the bowl as necessary.
Using a scoop, place 1-inch dough balls on parchment-lined baking sheets, ensuring they are spaced approximately 2 inches apart. Gently press down each ball with the bottom of a glass.
Immediately after removing them from the oven, toss the hot cookies in the measured powdered sugar to coat, then transfer them to a cooling rack.