12 hours later, the poolish should have doubled in size and have lots of air bubbles. This is a great sign that the poolish is mature, active, and ready to be baked with.
In a large mixing bowl, add the poolish, bread flour, and "00" pizza flour.
In a liquid measuring cup, combine warm, filtered water (78° F) and salt. Allow the salt to melt into the water.
Gradually add the water into the poolish and flour mixture, kneading everything together with your hands until the dough is combined and shaggy, about 8-10 minutes.
Next, transfer the dough onto the countertop and begin kneading the dough again for 1-2 minutes until it begins to come together and all of the big clumps of flour are worked out.
Once the dough begins to come together, perform 5-10 slap-and-folds. Slapping and folding is a technique of picking up the dough from its center and lifting it off the counter, then quickly slapping the dough back onto the counter. You are essentially folding the dough over itself in a slapping motion. This process adds a lot of strength to the dough.
Once the dough has formed a shaggy ball shape, tap a little bit of olive oil on the top, and set the dough aside to rest on the countertop for 15 minutes uncovered at room temperature.
After 15 minutes, gently fold the dough over itself, rotating the dough with every tuck-and-fold.
Perform 4-5 tuck-and-folds and then begin pushing and pulling the dough, scooping your hands slightly under the dough, until the dough is round and smooth on top. Be careful not to overwork the dough. Once it is smooth allow it to rest.
Next, tap the top of the dough with a little bit of olive oil and cover with a warm, damp tea towel for 1 hour.
After one hour, the dough should have risen and expanded.
Using an oiled bench scraper or knife, cut the dough into four equal pieces and use the same push-and-pull technique to form the dough into small, smooth balls.
Place the dough onto a lightly oiled sheet pan 3-4 inches apart from one another.
Allow the dough to rise with a warm, damp tea towel over them for 1-2 hours. They should double in size.
Once the dough is done rising, use a floured spatula and quickly scoop up the dough and place it into a bowl of flour.
Remove the dough from the flour and transfer it onto a pizza peel, sprinkled with semolina flour. This is where you will begin shaping the dough.
Begin gently pressing down in the center of the dough. When the dough is slightly flattened in the middle, use one hand to hold the dough down and the other to gently pull the side of the dough up and out, rotating the dough in 30° increments. Do this very gently. This will help keep the dough round, while gently stretching it out. Make sure to not crush the outer 1 inch of the dough.
Once the dough is about 12-14 inches in diameter, evenly spread a thin layer of tomato sauce and top with mozzarella cheese and any other toppings you like. I like adding thin-sliced shallot and prosciutto to mine. Note: I like to add my herbs after I bake the pizza because I think it keeps a stronger flavor. However, if you want to add basil before the baking process, drizzle a tiny bit of olive oil on each basil leaf to keep them from burning. Once your pizza is dressed with toppings, transfer the pizza off of the pizza peel onto the preheated pizza stone either on the grill or in the oven, and bake.