Special equipment: a ricer
Set a pizza stone or baking sheet on an oven rack in the bottom-third position and preheat to 500 degrees F. Divide the pizza dough into 2 balls. Spray a baking sheet with cooking spray and press each ball out into a thin 10-inch round. Put the baking sheet on the preheated stone and parbake until the dough just starts to brown on the bottom and edges, about 10 minutes for a softer crust or about 15 minutes for a crisper crust. Remove and let cool slightly.
Combine the mozzarella, ricotta, garlic, 1/4 teaspoon salt and crushed red pepper in a small bowl. Toss the mushrooms, olive oil, thyme and 1/4 teaspoon salt together in another small bowl.
Dollop the cheese mixture evenly on the 2 pizza crusts and spread out, then divide the mushrooms between them. Bake the pizzas until the crust is golden brown and the cheese browns in some spots, 8 to 10 minutes. Cut each into 4 pieces and serve.
Cover the potatoes with water in a medium pot. Bring to a boil and cook until fork-tender, about 25 minutes; remove. Once the potatoes are cool enough to handle, remove the skin and work the potatoes through a ricer set over a large bowl (should have about 2 cups). Set aside.
Stir together the warm water, agave and yeast in a measuring cup or small bowl. Let sit until a small layer of foam develops at the top, 3 to 5 minutes. (If this doesn't happen, discard and try again with new yeast.)
Add the potatoes, rice flour, tapioca starch and 3/4 teaspoon salt to the bowl of a stand mixer fitted with the paddle attachment. Mix on medium speed until the mixture is combined and forms a fine, crumbly meal. Continuing to mix on medium, add the egg white and oil, slowly drizzle in the yeast mixture and mix until the dough comes together (it will be slightly tacky). Cover the bowl tightly with plastic wrap and set in a warm place until the dough increases by half, about 1 1/2 hours.
Form the dough into 2 or 4 balls, for small or medium pizzas, then either cook them as desired or wrap them well and freeze for up to 1 month. Thaw frozen dough at room temperature, then shape and cook.
The secret ingredient in this easy-to-work dough is potato-it provides just the right texture and flavor as well as potassium. You'll need a ricer to ensure smooth potatoes for your dough, but we love this gluten-free recipe so much that we think you'll agree it's worth the small investment. Keep parbaked pizza shells on hand for quick weeknight meals. Roll the dough balls into rounds and bake on a preheated pizza stone or baking sheet at 500 degrees F for about 10 minutes for a softer crust, about 15 minutes for a crisper crust. Remove and let cool. Wrap the pizza shells well and freeze for up to 1 month. When ready to serve, add your favorite toppings to the frozen pizza shell and bake on a preheated pizza stone or baking sheet at 500 degrees F until hot.
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