In a large bowl, mix together the water, sourdough discard, salt, and oil. Mix until combined.
Add the flour slowly, about ½ cup at a time, and mix it in using a whisk.
When the dough becomes too difficult to mix with a whisk, use your hands to combine it until it has a shaggy consistency, but all ingredients are fully incorporated.
Cover the dough with plastic wrap, and let it sit for 6-8 hours or overnight at room temperature. The dough should double in size, and you will see bubbles if you use a glass bowl.
Once the dough doubles in size, perform one set of stretch and folds. Pull up a piece of the dough and stretch it over the top of the dough ball. Turn the bowl and repeat until the whole ball of dough is folded.
Cover the dough and place it in the fridge for 1–4 hours. Note that you can skip the refrigeration if time does not allow. If you do skip the refrigeration, then the bulk ferment in Step 4 is even more important and you may need to allow a bit more time. See Note 1.
Remove the dough from the fridge and let it come to room temperature for 30 minutes.
Sprinkle some flour on a clean surface. Then, divide the dough into two halves and roll each half into a disk shape. Use a rolling pin to flatten the dough until it becomes a circle approximately 1/4 inch thick. If required, you may use your hands to stretch the dough after rolling it out so that it maintains a circular form.
Preheat the oven to 450°F (232°C). Place a pizza stone in the oven while it preheats. This will ensure the crust is crispy and the cheese is melted to perfection. See Note for tips on baking the pizza in a cast iron pan instead of on a baking stone.
Once the oven is heated, using oven mitts, cautiously remove the pizza stone and sprinkle some flour or cornmeal on it. Then, carefully place your prepared dough on the stone.
Add your toppings to the pizza and bake for 10–15 minutes. Turn oven to broil, and broil for 2 minutes to brown the crust and toppings.
Let the pizza cool slightly before cutting and enjoy!