In the bowl of a stand mixer (e.g. KitchenAid), dissolve the yeast in the water. Add the vegetable oil, olive oil, cornmeal, and half of the flour. Beat for 10 minutes. Attach the dough hook and mix in the remaining flour. Knead for several minutes with the mixer. (Note: because the dough is very rich and moist, it would be difficult to do this by hand.)
Remove dough and place on a clean countertop. Cover with a very large metal bowl and allow to rise until double in bulk. Punch down and allow to rise again. Punch down a second time and you are ready to make pizza!
Oil your deep-dish pizza pan. Depending on the size of your pan, place some dough in the pan and push it out to the edges using your fingers. Put in enough dough so that you can run the crust right up the side of the pan. Make it about 1/8-inch thick throughout the pan.
Place the cheese in tile-like layers on the bottom of the pie. Next put in the tomatoes and the basil, oregano, garlic, and salt, reserving the Parmesan cheese for the top. Drizzle olive oil over the top of the pie and you are ready to bake.
Before you put on the Parmesan cheese and olive oil drizzle, you might like to add any or all of the following:
Bake the pie in a 475F oven until the top is golden and the crust a light golden brown, about 35 to 40 minutes.
- Yellow onions, peeled and diced
- Mushrooms, sliced
- Green sweet bell peppers, cored and sliced thin