Add flour, baking powder, and salt to a medium bowl. Whisk to combine. Set aside.
Cream together butter and sugar until light and fluffy, about 3 minutes. Add egg until well-combined. Slowly spoon in flour mixture mixing on medium speed until well-combined, then add vanilla and mix just until combined.
Scoop cookie dough by the tablespoon onto a large baking sheet, leaving about 2-inches between each cookie. Press down on cookie dough ball lightly with the palm of your hand or the bottom of a glass until about 1/2-inch thick. Bake 10-13 minutes until lightly browned.
For the roundest of cookies, you can roll them between your palms before dropping onto the baking sheet. Then, lightly press as directed before baking.