In a food processor, process sugar for 30-45 seconds to make superfine sugar (not powdered!)
Add in cold butter pieces and process for another 30-45 seconds. Until the butter and sugar are just combined.
Add in egg and vanilla extract. Process until just combined. You may need to scrape down the sides at least once.
Add in flour, baking soda and baking powder. Process until combined.
Divide dough in half. Take half of dough and place in-between two large pieces of parchment paper. Roll dough into a flat layer about an 1/8th inch think. Do the same with the other half. Refrigerate the flattened dough for at least 1.5 hours.
Cut out desired cookie shape* and place on a parchment lined cookie sheet*.
Bake for 20 minutes, on the second to lowest rack, at 300°F, or until edges just start to turn golden. Any scraps of dough leftover can be rerolled and refrigerated while the other cookies are baking. Try to use a cold baking sheet for every new batch.
Frost or eat plain! Both ways are delicious!