Preheat oven to preheat for 400 degrees.
While the oven heats, add gluten-free flour, coconut flour, sea salt, dried basil, garlic powder, and onion powder to bowl of food processor. Pulse 4-5 quick pulses to blend ingredients.
Add in the cubed butter pieces and pulse until you have a small crumbly texture (see photos), then gradually add in the icy water until mixture comes together, do not over-blend.
Flour a clean, dry surface, using gluten-free flour or coconut flour, then turn the mixture out and use your hands to form a 2" round, flat form. Wrap the dough in plastic wrap and put in refrigerator for 20-30 minutes (or longer).
While the dough refrigerates, peel and thinly slice sweet potatoes and beets. Then slice onions and set aside.
After 30 minutes, roll the dough out on to your floured surface to create a thin (approx 1/8"-1/4") 10" circle.
Layer the center of the dough with the sliced onions, then add a layer of sweet potatoes, then beets, reserving the most consistent and attractive beets and sweet potatoes to alternate for the top later. Make sure to leave about 1 1/2"-2" border around the outside edge of the dough.
Sprinkle with goat cheese and crushed garlic, then gather the edges of the dough, and fold them over the inner fillings. Bake for about 40 minutes or until beets and sweet potatoes are soft and cooked through. Let cool 5-10 minutes, then serve.