Whisk together the gluten-free flour, baking powder, and salt. Set aside.

Combine butter and sugar in the bowl of a stand mixer. Mix, on medium speed, until a thick paste forms, about 30 seconds. Stop mixer. Scrape down bottom and sides of the bowl. Mix again for 10 seconds.

Stop mixer and add egg and vanilla extract. Mix, on medium speed, until combined, about 30 seconds. Again, stop the mixer and scrape down the bottom and sides of the bowl. Mix again for 10 seconds.

With the mixer off, add the whisked gluten-free flour mixture. Mix, on medium-low speed, until a dough forms.

Turn the dough out onto a lightly floured counter and pat into a round. Wrap with plastic wrap and chill at least 45 minutes. (Dough can be chilled for several days).

Adjust oven rack to upper middle and lower middle positions. Preheat oven to 350 degrees F. Line to baking sheets with parchment paper.

Remove dough from the refrigerator and allow it to sit on the counter for about 15 minutes. Dust counter with gluten-free flour and roll out dough, about 1/4-inch thick. (If dough cracks, it's too cold.)

Cut into shapes with a cookie cutter. Place cookies onto a parchment-lined baking sheet. Sprinkle with colored sugar if desired.

Bake until edges are golden brown, about 12 minutes for 3-inch cookies. Rotate pans halfway through baking.

Allow cookies to cool on the baking sheet for about three minutes before transferring to a wire rack to cool completely.

Prepare Frosting: In a small bowl, beat together powdered sugar, butter, vanilla, and milk until smooth and creamy. If frosting is too thick, add an additional teaspoon of milk. Divide frosting between bowls and color if desired.

Frost cool cookies with frosting. Store, covered, for up to four days. Or freeze cookies in a freezer container.