Step 1Dissolve the yeast with the sugar in 1/2 cup of the water and set aside until foamy.
Step 2In a large mixing bowl, combine the remaining 3/4 cup warm water, the olive oil and yeast mixture. Stir in the flour, 1 cup at a time, and salt mixing until the dough begins to come together in a ball. Spoon the dough onto a floured board and knead it until it's smooth, elastic and no longer sticky, about 5 minutes. Place the dough in an oiled bowl, cover it with plastic wrap and set it aside in a warm place until it has doubled in size, about 1 hour. It is then ready to use.
Step 1Heat the oil in a heavy pot over medium-low heat. Add the garlic, onions, bell pepper, carrots and celery and cook until the vegetables are soft, about 10 to 15 minutes.
Step 2Add the tomatoes with the liquid, the red wine, oregano, basil, parsley and sugar. Bring the sauce to a boil, cover and simmer until it's thick, about 30 minutes.
Step 3Season the sauce to taste with salt and pepper. Transfer it to a bowl to cool, cover it with plastic wrap and set it aside. Makes 3 cups.
Step 1Divide the dough into 2 equal balls. Roll 1 ball out on a floured board into a thin circle, about 12 to 14 inches in diameter.
Step 2Dust a round pizza baking pan or baking sheet with cornmeal and slip the rolled dough onto the prepared pan.
Step 3Spoon 1 cup of sauce in a thin coating on the pizza, spreading it with the back of a spoon to within 1 inch of the edge. Sprinkle the pizza generously with half the mozzarella and Parmesan cheese. Drizzle 1 tablespoon of oil over the top. Repeat with the second ball and ingredients to make a second pizza.
Step 4Bake the pizzas in batches on the lowest rack of the oven until the crust is crisp and brown and the cheese is hot and bubbling, 10 minutes. Serve immediately.