In a medium sized mixing bowl, mix the gluten free flour and baking powder together. Set this bowl aside.
In the stand mixer with the paddle attachment, cream the butter and sugar together until well combined.
Add the egg and vanilla extract into the stand mixer bowl and mix until just combined.
Slowly begin adding the dry ingredients in the medium sized mixing bowl into the stand mixer bowl. Mix the gluten free sugar cookie dough until the dough begins to pull from the sides.
Remove ⅓ to ½ of the dough and place it on top of a piece of parchment paper. Roll the dough out to ⅜" thick and use the cookie cutter(s) to cut out the cookies. Place these cookies onto a prepared baking sheet, making sure to not overcrowd the pan.
Preheat the oven to 350° F. Place the cookies on the baking sheet into the freezer while the oven preheats, or for at least ten minutes.
Once the oven is preheated, remove the cookies from the freezer and place the whole tray with cookies into the oven. Bake for 9-11 minutes or until the tops of the cookies do not appear wet.
While the cookies are cooling, roll out, cut, and freeze the next round of cookies. If you don't have multiple cookie sheets, place the cookies on parchment paper to act as the baking sheet. Once frozen for at least 10 minutes, place the cookies into the oven to cook. You can place the parchment paper onto the partly cooled baking sheet from the last round of cookies baked. Repeat these steps until all the cookies have been baked.