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.
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 kneed the ball of dough until it is no longer sticky.
Let the dough rise in an oiled bowl, sealed with plastic wrap, for 45 to 60 minutes in a warm place, until it is doubled in bulk. Punch it down and kneed 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 to 20 minutes before filling. Preheat the oven to 500 degrees. While the dough is rising, prepare the filling.
Cook the crumbled sausage until it is no longer pink, drain it of its excess fat. Drain and chop the tomatoes. When the dough has finished its second rising, lay the cheese over the dough shell. Then 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 degrees. Then lower the temperature to 400 degrees and bake for 25 to 35 minutes longer.
Lift up a section of the crust from time to time with a spatula to check on its color. The crust will be golden brown when done. Serve immediately.