Mix the warm water and yeast in a small bowl to blend. Let stand until the yeast dissolves, about 5 minutes. Mix the flour and salt in a food processor to blend. Blend in the oil. With the machine running, add the yeast mixture and blend just until the dough forms. Turn the dough out onto lightly floured surface and knead until smooth, about 1 minute. Transfer the dough to a large oiled bowl and turn the dough to coat with the oil. Cover the bowl with plastic wrap and set aside in a warm draft-free area until the dough doubles in volume, about 1 hour. Punch the down dough and divide into 2 equal balls. (The dough can be used immediately or stored airtight in the refrigerator for 1 day.)
Position 1 oven rack in the center and the second rack on the bottom of the oven and preheat to 450 degrees F. Sprinkle the cornmeal over 2 rimless baking sheets. Roll out each piece of pizza dough into a 10 to 11-inch-diameter round. Transfer 1 dough to each prepared baking sheet.
Drizzle 2 teaspoons of oil over each pizza dough. Sprinkle the mozzarella over the pizza dough, dividing equaling and leaving a 1-inch border around each pizza. Arrange the tomato slices in a single layer over the cheese. Sprinkle with the Parmesan. Arrange basil leaves on top, drizzle with a little more olive oil and sprinkle garlic all over. Bake the pizzas until the crusts are crisp and brown on the bottom and the cheese is melted on top, about 15 minutes. Drizzle 1 teaspoon of oil over each pizza. Sprinkle with basil for garnish and salt. Cut the pizza into wedges and serve immediately.