Combine flour, cornmeal, yeast and sugar in the bowl of a stand mixer or food processor fitted with dough attachment. Pulse to combine ingredients.
Add water and melted margarine and process until a ball of dough is formed, scraping down the sides of the bowl when necessary.
Remove ball of dough from mixer or processor and knead for 1 minute by hand, then place dough in an oiled bowl, cover and set in a warm place to rise for 40 minutes to 1 hour.
If making your own tomato sauce, prepare that while the dough is rising.
For any raw vegetables that you are using in the pizza (for example, zucchinni, fresh tomato, onions), place them in a large strainer and sprinkle generously with with salt. Place the strainer over a bowl and set aside so that vegetables can release some of their liquid.*
When dough has risen, roll it out into a rectangle and spread with softened butter.
Fold rectangle of dough into thirds like a business letter, and fold in thirds again. Shape dough into a ball and return to oiled bowl to let rise again for 40 minutes to an hour.
While dough is rising for the second time, preheat oven to 425.
When dough has risen, roll out into circle large enough to line a cast iron skillet or 9 inch round cake pan.
Press dough into bottom of pan and up the sides of the pan to form a deep crust.
Sprinkle dough with shredded cheese (if using) and top with 3/4 cup of tomato sauce.
Arrange vegetables on top of sauce in layers, sprinkling with pepper and salt (omitting salt on the layers of raw vegetables that have already been salted).
Top pizza with remaining tomato sauce.
Place in oven and cook for 30 minutes until crust is firm and sauce is bubbling.
Let sit for 10-15 minutes before cutting and serving.