For this small amount of dough, I find a hand mixer works better than my Bosch with a paddle. There just isn't enough dough for that kind of mixer to do a good job. You may have another type of mixer that can mix small amount of sugar cookie dough well, and that is fine to use that too.
In a large glass bowl, beat the butter and refined coconut oil together well. Add the sugar and cream together.
Add the egg and vanilla and mix well.
Add the powdered sugar, xanthan gum, baking powder, sea salt, and psyllium husk and mix. Add the flour and mix until combined.
With a spatula, scrape dough onto some plastic wrap. Press the dough together using the plastic wrap until the dough is pressed well together in a rectangle. Wrap up tightly and place in refrigerator for at least 30 minutes.
Preheat oven to 350 degrees. Prepare baking sheets with silicone liners AND parchment paper on top of the liner.
On parchment paper on your counter, sprinkle some gf all purpose flour lightly. Take about half the dough, sprinkle some more gf flour on top, and roll it out to about 1/4 inch thickness adding tiny amounts of flour as needed.
Use cookie cutter shapes to cut out the dough. Place on the prepare pans. The dough is a bit soft, so if it sticks to your parchment paper, you can try using a metal spatula to gently lift the dough onto the prepared pan. Continue gathering scrapes and reforming the dough to roll out and cut out more shapes until the dough is used up.
When you have filled up one pan, bake it for 11-12 minutes or until the sides of your cookies are a little firm(just don't want them to press in still when lightly touched). Cool 2-3 minutes on the baking sheet before removing to a cooling rack. This is an important step, you need the cookies to finish "cooking" out of the oven. Then place the cookies on a cooling rack to finish cooling. When completely cooled, frost and decorate as desired. (While your first batch is baking, roll and cut out the rest of the dough)
Frost cookies as desired using my buttercream frosting or another of your choice. Once frosting is completely dried, you can store in a zip baggie or air-tight container for several days(if your family hasn't consumed them all that is!)