Make the dough: Combine the flour, cornmeal, salt, yeast, olive oil, melted butter, vegetable oil and warm water in the bowl of a stand mixer fitted with the dough hook. Mix on medium speed until the dough comes together and pulls away from the side of the bowl but still sticks to the bottom, about 3 minutes. Reduce the mixer speed to low and knead 5 minutes. Transfer the dough to a lightly oiled bowl and turn to coat. Tightly cover with plastic wrap and let rise in a warm place, 1 hour.
Meanwhile, make the sauce: Heat the olive oil in a medium saucepan over medium heat. Add the garlic and red pepper flakes and cook, stirring, until the garlic is slightly softened, about 1 minute. Add the tomato puree and 1 cup water. Stir in the oregano and 1 teaspoon salt. Bring to a boil, then reduce the heat and simmer, stirring occasionally, until slightly thickened, about 8 minutes.
Preheat the oven to 425 degrees F. Generously brush two 9 1/2-inch round deep-dish pizza pans (or 9-inch cake pans) with about 3 tablespoons olive oil each. Divide the dough in half; press each half into the bottom of a pan. Let the dough rest, 15 minutes. Push the dough down and press it up the sides of the pans with your fingers. Layer the cheese on top of each crust and spread each with 1 1/2 cups sauce.
Bake the pizzas until the crust is dark golden brown and the cheese is bubbling, 40 to 45 minutes (it will still be jiggly in the center). Sprinkle with parmesan (if using); let cool 15 minutes. Transfer to a cutting board and cut into wedges.
You can freeze the baked pizza for up to a month. Let it cool, then tightly wrap in plastic and foil. To reheat, unwrap and bake at 325 degrees F until hot and bubbling, 50 to 60 minutes.