Dough: Place flour, yeast, salt and sugar in a mixer fitted with a dough hook. While mixer is running, gradually add water, knead on low speed until dough is firm and smooth, about 10 minutes. Turn machine off. Pour oil down inside of bowl. Turn on low once more for 15 seconds to coat inside of bowl and all surfaces of dough with the oil. Cover bowl with plastic wrap. Let rise in warm spot until doubled in bulk, about 2 hours.
Sauce: Pour tomatoes into a strainer that has been fitted over a microwave proof bowl. Using your hands, crush the tomatoes. Press all juices into bowl. Set crushed tomatoes aside. Place bowl with tomato juices in microwave and cook on high until thickened to consistency of ketchup, about 20 to 25 minutes. Add crushed tomatoes to sauce. Cool to room temperature. Toppings: Slice some vegetables. Skewer onion slices to keep them together. Brush vegetable slices with olive oil. Sprinkle with salt and pepper. Place vegetables on hot grill pan. When done, set aside. Assembly: Preheat your oven to highest setting, 500 or 550 degrees. If using a pizza stone, preheat oven 1 hour ahead. Punch dough down, cut in half. On generously floured work surface, place one half of dough. By hand, form dough loosely into a ball, stretch into a circle. Using a floured rolling pin, roll dough into large circle until very thin. Don't worry if your circle isn't perfect. If you get a hole, pinch edges back together. To prevent dough from sticking to counter, turn it over and add flour as needed. Transfer dough to pizza peel sprinkled with cornmeal. Ladle tomato sauce on pizza dough. Add assorted vegetables. Bake 10 to 12 minutes or until golden.