Preheat the oven to 375 F/190 C.
In a stand mixing bowl, cream together the butter and sugar until JUST combined.
Scrape down the bowl with a rubber spatula. Then mix in the egg and vanilla. Scrape down the bowl again.
Mix in the flour, baking powder, corn starch, and salt until just combined and there are no more dry flour streaks.
Divide the dough in half. Place one half on a piece of parchment paper.
Press the dough down into a flat disk and place another sheet of parchment paper on top. Roll the dough to ⅛ inch thickness for thin cookies or ¼ inch thickness for thicker cookies.
Transfer the slab of dough still between the sheets of parchment on a baking tray and chill it in the freezer while you roll out the other half of dough in the same way.
Chill both trays of dough for 5-10 minutes or until it feels firm.
Then remove the top sheet of parchment paper. Cut out cookies with your desired cookie cutter. Place the cut cookies back on the baking tray. You can rework the dough 1-2 times but no more than that or they will shrink from being worked too much.
Freeze each tray of cut cookies until completely frozen solid, about 15-25 minutes.
Bake one tray at at time for 10-13 minutes depending on the size and thickness. They are done baking when the tops look matte, dry, and slightly wrinkled. Do not let the edges brown or they will be more crisp.
Allow the tray to cool completely on a wire rack before removing and decorating.