Start by adding 3 cups bread flour, sugar, and the yeast to a large bowl. Combine with a fork, then gradually drizzle the ice water into the bowl. Mix gently with a fork until there's no more dry flour.
Set the dough aside for 10 minutes. This autolyse rest period improves the bonds between starch, gluten, and water, creating a better dough in the end.
Add in the salt and 1 tablespoon oil and mix with your hands until just combined. Then place the dough on an oiled plate or baking sheet using the remaining vegetable oil, knead for 1 to 2 minutes until stretchy, and shape into a ball. Place the ball in a bowl sprayed with cooking spray, cover the bowl with plastic wrap, and refrigerate for 24 to 72 hours.
An hour before you're ready to bake the pizza, place your baking stone on an oven rack in the second highest position in your oven. Preheat the oven to 500 degrees.
Remove the dough from the refrigerator and cut in half, shape each half into a ball and place both on a baking sheet sprayed with cooking spray. Spray the balls with cooking spray as well and then cover with plastic wrap and let stand for about an hour while the oven is preheating.
Then take one of the balls and place on a well floured countertop or baking sheet. Gently flatten into an 8-inch disk using your fingertips. Leave the edges a bit thicker than the middle. Then gently stretch the dough using your hands, until it measures about 12 inches in diameter.
Add semolina or bread flour to the pizza peel, making sure it's well floured, then place the pizza dough on the peel and stretch a bit more until it's about 13 inches across.
Add pizza sauce, then Parmesan cheese, and finally the mozzarella cheese. Add any toppings, then slide the pizza carefully onto the pizza stone.
Bake for 10 to 12 minutes until the cheese is bubbly and golden brown. Add more semolina or flour to the pizza peel. Remove the pizza from the oven with the pizza peel and place on a wire rack for a few minutes before serving.
Repeat the steps for the second pizza.