In a large mixing bowl, whisk together the flours, xanthan gum, baking powder, salt, and spices.
In the bowl of a stand mixer with the paddle attachment, cream the butter. Then beat in the sugar.
Beat the eggs in until well incorporated.
Add the flour mixture and beat until combined, stopping to scrape down the sides of the bowl as necessary.
Divide the dough into two balls. Wrap each in plastic, flatten to a disc shape and refrigerate for one hour. If you've left it longer, leave it out on the counter for a few minutes to become workable again. It should be firm enough to hold its shape but soft enough to work with.
Preheat oven to 350° F. Line two 12- by 18-inch baking sheets with parchment paper.
Flour your work surface with any of the gluten free flours and roll out dough, one disc at a time. For the windmill cookie cutter I used, the dough needs to be ¼-inch (6 mm) thick to show the imprinted pattern. Otherwise, you could roll the dough to ⅛-inch (3 mm) thick.
Cut out shapes with a cookie cutter and place them on a parchment-lined pan.
Bake for 20 minutes (10 - 15 minutes for thinner cookies). Watch your cookies closely near the end of baking time. You're looking for browning around the edges. These cookies are good when they're well done but not burnt.