Preheat oven to 425 degrees F (220 degrees C). Grease a 15-inch pizza pan with cooking spray.
Stir all-purpose baking flour, garbanzo bean flour, cornstarch, tapioca starch, Parmesan cheese, baking powder, xanthan gum, Italian seasoning, oregano, and salt together in a bowl; set aside.
Dissolve 1 teaspoon of white sugar in lukewarm water in a small bowl. Sprinkle yeast over top, and set aside until foamy, 3 to 5 minutes.
Beat egg in a separate bowl with olive oil, vinegar, 1 teaspoon sugar, and garlic until smooth. Whisk yeast mixture into egg mixture and stir in flour mixture until no dry lumps remain. Press dough into prepared pan, leaving outer edge slightly thicker than the center.
Cook in preheated oven until dough has risen and slightly firmed, 10 to 12 minutes.
Once topped with your favorite toppings, continue baking at 425 degrees F (220 degrees C) until the crust is golden brown, 20 to 30 minutes. Remove pizza from pan and cook directly on the oven rack for 5 minutes to crisp crust, if desired.