Add and combine the all-purpose gluten-free flour, xanthan gum, baking powder, and salt.
In a separate bowl, add and combine the water, instant yeast, and egg. Then, beat the ingredients at low speed using a standalone mixer with the paddle attachment fitted. Slowly and in a steady stream, add the flour mixer. Then, increase the speed to medium and beat the dough for 2-3 minutes.
Transfer the dough to a greased bowl and cover it with plastic wrap, followed by a damp kitchen towel. Allow the dough to proof for 12-24 hours at room temperature.
Preheat the oven and pizza stone to 210°C (410°F).
Transfer the dough to a lightly floured surface and divide it into two equal parts.
Working with one dough at a time, shape the dough into a ball. Then, using your fingertips and knuckles, depress the dough at the center without touching the outer edge of the dough. Try to shape the dough into a 30 cm (12 inch) circle with your fingers without touching the circle's border. You want the outer crust of the pizza dough to be thicker than the center to achieve a bubbly crust. Note: To easily transfer the dough to the pizza stone, shape the dough on parchment paper and transfer the dough while it is still on parchment paper to the pizza stone to prevent tearing.
Now, spread the pizza sauce on the dough, leaving a 1 cm (½ inch) border around the dough. Then, add the mozzarella cheese.
Bake the pizza for 7-10 minutes or until the crust is slightly golden. Then let it rest for 3 minutes before cutting and serving.