After the dough has rested for at least an hour and risen, punch it down.
Divide the dough into two balls. (If you're not going to use both right away--which occasionally happens--wrap one in plastic wrap and refrigerate.)
Lightly flour a board or countertop.
Gently roll or stretch the dough until you have the desired size, shape, and thickness--but the thinner the better. (If you use a rolling pin, be sure to dust it with flour first, and keep turning the dough as you roll it out.)
Dust the pizza peel lightly with cornmeal and carefully put the rolled-out dough on the peel.
Top with tomatoes and mozzarella, leaving a 1 inch margin around the edges, and sprinkle with parmesan.
Tranfer the pizza from the peel to the stone: rest the front edge of the peel about an inch from the far side of the stone and then pull the peel out with short, quick jerks--the pizza should slide off smoothly (provided you used enough cornmeal).
Start checking the pizza after about 7 minutes--once the cheese is melted and the crust is golden brown, it's done.
Remove the pizza. The easiest thing to do is to slip the front edge of the peel just under the near side of the pizza and then use tongs to pull the pizza onto the peel.
Transfer the pizza to a large board or pizza pan. Sprinkle with basil and add a light swirl of extra virgin olive oil.
Cut into slices and serve.