In a separate bowl, combine flour, baking powder and baking soda. Whisk together, then pour into the butter mixture. Stir to combine.
Place remaining ½ cup of sugar in a bowl. Roll dough into 1–1½-inch balls and roll in sugar, making sure to coat all sides.
Place on a greased cookie sheet and make a crisscross on top of each ball using a fork. Bake for 8–9 minutes.
Let cookies sit on the cookie sheet for a few minutes, then remove to a rack to cool.