Place all-purpose flour, salt, and active dry yeast in a large bowl and stir with a wooden spoon or rubber spatula to combine.
Add water (110-117 degrees F) and 3 tablespoons of the extra-virgin olive oil and stir until no dry flour remains and a shaggy dough forms. Knead in the bowl a few times, sprinkling with a little more flour if needed, until a rough, sticky ball of dough forms. Tightly cover with plastic wrap and let rise at room temperature for 2 hours.
After 2 hours, the dough will have puffed and doubled in size. Refrigerate the bowl of dough at least 8 hours and up to 24.
Drizzle 2 tablespoons of the extra-virgin olive oil onto a 13x18-inch rimmed baking sheet. Remove the bowl of dough from the refrigerator and use your hands to transfer the dough to the prepared baking sheet. Turn to coat in the oil, then gently press and flatten the dough until about 1-inch thick. (The dough will not reach the edges of the baking sheet.)
Cover loosely with plastic wrap and let rest for 10 minutes.
Uncover the dough and use your fingertips to stretch the dough to the edges of the baking sheet. If it starts to shrink back, let it rest for a few minutes, then try again. Cover again and let rest until puffed and slightly risen, about 25 minutes.
Preheat the oven to 475 degrees F. Add sauce, cheese and toppings on top of dough. Bake 20 minutes.