Prepare the pizza dough, dividing into four portions after the first rising. When the dough has risen for the second time, place the oven rack in the lowest position, center a pizza stone over it, and preheat the oven to 475 degrees.
Roll or stretch each of the dough balls out to a 12-inch circle about ¼-inch thick with a slightly thicker border around the edge. Brush each circle lightly with some of the olive oil. Working with one crust at a time, sprinkle a pizza peel of flat baking sheet generously with the cornmeal. Place the circle of the dough on the cornmeal and spoon ¼ cup of pizza sauce over the dough, leaving a thin border around the edge. Scatter ¼ of the mozzarella over the tomato sauce. Sprinkle the pizza lightly with salt and scatter some of the basil over it. Drizzle a little of the remaining olive oil over the cheese.
Pull the oven rack out partially and slide the pizza onto the stone. The best way to do this is to bring the peel down to the stone and lift the peel until the pizza starts to slide. Once the crust makes contact with the stone, pull the peel quickly from the pizza. Make sure you center the peel and pizza over the stone so the pizza doesn’t over-hang the stone when you remove the peel. Push the rack back in, close the oven and bake until the pizza is golden brown underneath and the cheese is melted, about 8 minutes. Remove the pizza by nudging it onto the peel with a spatula or pair of tongs. Allow a few minutes for the stone to reheat before cooking another pizza on it.