In the bowl of a stand mixer on medium speed, beat the softened butter and sugar until fully incorporated. Reduce the speed to low and add the extracts and the egg. Mix just until blended.
In a separate mixing bowl, whisk together the salt, baking powder, rice flour, tapioca starch, potato starch, and xanthan gum.
With the mixer on low speed, slowly add the dry ingredients, scraping down the bowl as necessary. Mix just until the dough comes together.
Scrape the dough out onto a sheet of plastic wrap, and wrap tightly before refrigerating for at least 1 hour. This will help your butter to solidify and help your cookies to keep their shape while baking.
When you are ready to bake, preheat your oven to 350 degrees F and line your baking sheets with parchment paper.
Working with a quarter of the dough at a time, roll the dough to about 3/8-inch thick between two sheets of plastic wrap, dusting with a small amount of sweet rice flour if necessary. Cut to desired shapes and place on prepared baking sheets, leaving 2-inches between cookies. You can re-roll the scraps until all the dough has been used.
Bake in preheated oven for 8-12 minutes, depending on the size of your cookies. The cookies should just barely be turning brown around the edges, and have just a light brown colour on the bottom of the cookie.
Let cookies sit on the baking sheet for 5 minutes before removing to a cooling rack. Allow cookies to cool completely before decorating with icing or storing in an air-tight container.