1. For dough, sprinkle yeast and sugar into warm water in small bowl; let stand until foamy, about 5 minutes.
2. Mix flour, oil and salt in a large bowl; make a well in the center and add yeast mixture. Stir to form a soft dough, adding more flour if necessary. Turn onto a floured board and knead until dough is supple and elastic, 7 to 10 minutes. Transfer to a large bowl, cover and let rise in a warm spot until dough has doubled, about 1 hour. Punch down.
3. Roll dough to a 15-inch circle. Transfer to an oiled 14-inch pizza pan, folding the excess over to make a small rim. Spread with pizza sauce; sprinkle with all but a handful of the mozzarella cheese. Sprinkle with meats and vegetables. Top with remaining mozzarella and Parmesan cheese. Let rise in a warm spot about 25 minutes.
4. Heat oven to 475 degrees. Bake pizza until crust is golden, about 25 minutes. Let stand 5 minutes before slicing.