Pour the warm water into a large mixing bowl and dissolve the yeast with a fork.
Add 1 cup of flour, all of the cornmeal, salt, and vegetable oil, and mix well with a spoon.
Continue stirring in the rest of the flour 1/2 cup at a time, until the dough comes away from the sides of the bowl. Flour your hands and the work surface and knead the ball of dough until it is no longer sticky.
Let the dough rise in an oiled bowl, sealed with plastic wrap, for 45-60 minutes in a warm place, until it has doubled in size.
Punch it down and knead it briefly.
Press it into an oiled 15-inch deep dish pizza pan until it comes 2 inches up the sides and is even on the bottom of the pan.
Let the dough rise 15-20 minutes before filling.
Preheat the oven to 500°F.
While the dough is rising, prepare the filling.
Cook the sausage until it is no longer pink and drain the excess fat.
When the dough has finished its second rising, lay the cheese over the dough shell.
Distribute the sausage and garlic over the cheese.
Top with the tomatoes.
Sprinkle on the seasonings and Parmesan cheese.
Bake for 15 minutes at 500°F, then lower the temperature to 400°F and finish baking for 25-35 minutes longer.
Lift up a section of the crust from time to time with a spatula to check its color. The crust will be golden brown when done.