FOR THE PIZZA: Process flour, sugar, yeast, and salt in food processor until combined, about 3 seconds. With processor running, slowly add cold water and oil and process until dough forms sticky ball that clears sides of bowl, 30 to 60 seconds.
Transfer dough to lightly oiled counter and knead until smooth, about 1 minute. Shape dough into tight ball and place in greased bowl. Cover bowl with plastic wrap and let dough rise at room temperature until almost doubled in size, 2 to 21/2 hours. Cover bowl tightly and refrigerate for 3 days.Minimum 1 day.
Cut dough ball in half.Return 1 dough ball to bowl and cover with plastic.Wrap the other ball and refrigerate until needed.Let the ball in the bowl sit for 1.5 hours room temperature.Preheat your oven to 450 to 500 with pizza stone in it.Stone must heat slowly.
After dough comes to temp, Transfer dough to lightly floured counter.Coatdough ball lightly with flour and gently flatten into 8-inch disk using your fingertips. Using rolling pin, roll dough into 12‑inch circle, dusting dough lightly with flour as needed. (If dough springs back during rolling, let rest for 10 minutes before rolling again.).
Cut parchment paper in rough circle.Leave enough room to grab paper when pizza is on it.Sprinkle paper with cornmeal and put crust on paper.Prick crust with fork and bake on pan for 2-3 minutes.
Pull dough from oven and assemble pizza.
Slide pizza and paper onto stone using pan for transfer.