In the bowl of a stand mixer fitted with the dough hook, whisk the bread, rice, and soy flours, and the yeast.
Add 1-½ cups of the water, and knead on low speed until the dough comes together and there is no more dry flour in the bowl, about 3 minutes.
Add the salt and olive oil, knead on medium speed. While kneading, add the remaining ¼ cup of water a little at a time.
Once all the water has been absorbed, 2 to 3 minutes, increase he speed to medium high. Knead until the dough is smooth, elastic, and shiny, about 10 minutes more.
Transfer dough to a large bowl lightly coated with vegetable oil. Cover tightly with plastic wrap, and let rise in the fridge (39℉ to 41℉) for 24 hours, or until the dough has tripled in size. (See notes below)
Turn the dough out onto a lightly floured surface, allowing it to gently release from the bowl. Using a dough scraper or a knife, cut it into 6 equal pieces, weighing around 165 grams (5.8oz.) each. For this we use rice flour. It works better and the dough doesn't seem to absorb it as much.
Working with one piece at a time, take the four corners and fold them into the center to attach. Do not flatten.
The dough will tighten up and take on a round shape. Repeat with the remaining dough pieces.
Place roughly shaped dough balls on a greased baking sheet. Leave enough space between the pieces so that they can double their size without touching. Sprinkle the dough lightly with rice flour, and cover the baking sheet lightly with plastic wrap.
Set aside to rise at room temperature until the dough has doubled in size, 2 to 3 hours.
While the dough is rising, prepare the pinsa toppings of your choice. Set aside.
When ready to form the dough place one dough ball on a well-floured surface, then sprinkle more flour on top.
Starting from the center and working toward the edges, work the dough into an oval by pressing your fingers flat into the dough, gently stretching and pulling, until it measures approximately 6 inches by 10 inches. If the dough is resistant, let it rest for a few minutes before trying again.