Wash hands with soap and water for 20 seconds.
Do not taste or eat any raw dough or batter made with uncooked flour and/or raw eggs.
In a stand mixer with a dough hook or food processor, combine yeast, water, and oil; let rest 5 minutes.
In a medium bowl, combine the flours, sugar, and salt; whisk until combined. With the machine on, add dry ingredients slowly to the mixer or processor to combine and form dough. If the dough is too dry, add a tablespoon or two of water. If the dough is too wet, add flour 1 tablespoon at a time until the dough is no longer sticking to the sides of the bowl. The stickier the dough, the better the texture of the pizza crust.
Knead the dough for 1 minute.
Oil a large bowl and add the dough. Turn over the dough to coat with oil. Cover the bowl with a towel and let rise for 1 hour.
If using, place a pizza stone, pizza steel, or inverted rimmed baking sheet in the oven. Heat the oven to its highest setting500°F–550°F. During this time, prep the pizza toppings.
Line a pizza peel, rimless cookie sheet, or the back of an inverted sheet pan with parchment paper or sprinkle with cornmeal; set aside.
Cut the dough into two pieces. Use a scale if you want to be exact. Form the dough into two balls.
Rub a work surface and hands with a little olive oil. The olive oil keeps the dough from sticking and also encourages a golden and crispy crust.
On the work surface, press the dough down into a large flat disc using the palm of your hand. Next, use the middle three fingers on each of your hands (not a rolling pin) to press the dough out from the center, widening the flat disc into a large circle about 6 inches across and about ½ inch thick.
To stretch, carefully pick up the dough and hold it with both hands on one edge of the dough, letting the rest of the dough hang down. Keep the top of the pizza dough facing toward you to keep an eye on thickness. Gravity is going to do some of the stretching work as you gently rotate the dough in one direction, like turning a wheel. Slowly pull the dough from hand to hand as the dough hangs down. Working quickly, stretch the pizza until it’s about 12 inches in diameter and about 1/3 of an inch thick.
Carefully move the stretched pizza dough to the prepared pizza peel, cookie sheet, or sheet pan. Pinch thin or torn areas closed by pressing around them to bring the dough together to cover the area.
Wash hands with warm running water and soap after handling uncooked flour and/or raw eggs. Clean all surfaces and utensils they have touched.
Top pizza with sauce and desired toppings. Brush the crust with olive oil right before it goes in the oven, and if desired, again as soon as it comes out.
Transfer pizza to the preheated pizza stone, pizza steel, or inverted rimmed baking sheet in the oven and bake for 6–12 minutes, depending on the oven temperature, until the crust is golden brown. When the pizza is done, transfer it to a baking rack, rather than a flat surface, to prevents teaming and keep the crust crisp.
Wrap cooled pizza tightly in plastic wrap and store in the refrigerator.