Dissolve salt, sugar, and yeast in the warm water and allow the yeast to proof. ("Proofing" the yeast is testing it for viability. It will develop foam which looks like the head of a beer. If it doesn't proof, the yeast is dead and should be discarded.) Proofing takes about 15 minutes.
Place flour in a food processor fitted with a dough blade, and through the feed tube with the food processor running, slowly pour the proofed yeast mixture, until the dough comes together and is a cohesive mass. Transfer the dough to a floured board, and knead for about 5 minutes. Place in a bowl, cover with a clean dish towel and allow dough to rise, so that it roughly doubles in volume. (This will take about 30 minutes to an hour). The dough has risen enough if you make an indentation with your finger and it does not spring back.) Punch the dough down and allow it to rise again. (Allowing the dough to rise a second time gives it a finer texture.) Note: It will not rise as much the second time.
While the dough is rising, prepare the pizza topping. Heat 1 tablespoon of the oil over medium high heat in a large sauce pan and saute garlic and onions. Add parsley, salt, tomatoes, and basil. Cook for about 20 minutes to allow flavors to integrate. Mix with an immersion blender, then set aside briefly.
Preheat oven to 450 degrees F. Divide the dough in half and stretch out 2 (14-inch) circles. Transfer them to pizza stones sprinkled with cornmeal. Top with the tomato sauce as you would a pizza topping. Lay an even amount of mozzarella cheese slices on each. Roll up and seal ends. Bake for 15 to 20 minutes, or until the dough is nicely browned.