Combine the flours, starches, and xanthan gum with the baking powder and salt in a medium bowl. Set that aside and combine the sugars, shortening, and butter until creamy. Then add in the eggs and vanilla.
Slowly add in the flour mixture, then split the dough in half, wrap it in plastic wrap, and refrigerate it for an hour.
Once the dough is cooled, roll it out onto a floured surface (remember to use gluten free flour!) and cut into shapes. Place on a greased baking sheet and bake for 8-10 minutes in a 350 degree oven.
Remove the cookies carefully from the baking sheet immediately after they come out of the oven and put them on a cooling rack. Once they're nice and cool, you're ready for icing! I used royal icing (1 egg white and 1 ¾ cups powdered sugar), but any icing will do.
This recipe makes about 50 medium-sized cookies, and I ended up needing to triple the icing recipe to make enough. Once the cookies are iced, you'll need to lay them flat in a single layer for a few hours until the icing fully solidifies. Then you can stack them up to store them if you want to.