Preheat oven to 350°.
Cream together the butter and sugar in the bowl of a stand mixer for a full 3 minutes.
Scrape sides and add in vanilla and egg. Mix until combined.
Add flour and baking powder to the bowl. Mix slowly at first gradually getting faster until the dough comes together. The texture should be like Playdoh. Add a little flour or water if needed to get it to a soft, pliable consistency.
Turn out onto a floured surface. Use a rolling pin and roll until about 1/4 inch thick. (The cookies will not rise while baking, they will not get thinner while baking. Roll out to your desired FINISHED thickness.)
Use varying sizes of circle cookie cutters and cut circles out of the dough.
Press the backside of the dough onto the top of a wooden skewer. Be sure to press it on well.
Transfer to a silicone lined cookie sheet.
Bake at 350° for 8 minutes or until the centers are puffy and no longer glossy.