Step 1: Prepare the Dough. In a large bowl, combine warm water, sugar, and yeast. Let stand for 5-10 minutes until foamy. In a separate bowl, whisk together flour, cornmeal, and salt.
Step 2: Combine Wet and Dry. Add the melted butter and olive oil to the yeast mixture. Gradually add the dry ingredients to the wet ingredients, mixing until a shaggy dough forms. Turn out onto a lightly floured surface and knead for 8-10 minutes until smooth and elastic.
Step 3: First Rise. Lightly grease a large bowl with olive oil. Place the dough in the bowl, turning to coat. Cover with plastic wrap and let rise in a warm place for 1.5-2 hours, or until doubled in size.
Step 4: Prepare the Sauce. While the dough rises, heat 1 tablespoon olive oil in a saucepan over medium heat. Add minced garlic and sauté until fragrant (about 1 minute). Stir in crushed tomatoes, oregano, basil, and red pepper flakes (if using). Season with salt and pepper. Bring to a simmer, then reduce heat and cook for 15-20 minutes, stirring occasionally, until slightly thickened. Set aside to cool.
Step 5: Prepare the Pan. Preheat oven to 425°F (220°C). Generously grease a 10-inch deep-dish pizza pan or a cast iron skillet with 2-3 tablespoons of melted butter.
Step 6: Shape the Dough. Punch down the risen dough and transfer it to a lightly floured surface. Roll the dough into a large circle, about 14-16 inches in diameter, ensuring it's thin enough to line the bottom and sides of the deep dish pan with some overhang.
Step 7: Assemble the Pizza. Carefully transfer the rolled dough into the prepared pan, pressing it firmly into the bottom and up the sides. Ensure there are no air bubbles. Trim any excessive overhang, leaving about a ½-inch border.
Step 8: Layer the Filling. Arrange half of the sliced mozzarella cheese directly on the bottom of the crust. Add any meat toppings (sausage, pepperoni), then vegetables (bell peppers, mushrooms). Top with the remaining mozzarella cheese. Sprinkle with grated Parmesan.
Step 9: Add the Sauce. Spoon the cooled tomato sauce evenly over the top of the cheese and toppings, spreading it almost to the edge of the crust.
Step 10: Bake. Bake for 40-50 minutes, or until the crust is golden brown and the sauce is bubbly. If the crust edges brown too quickly, you can loosely cover them with foil.
Step 11: Rest and Serve. Carefully remove the pizza from the oven and let it rest in the pan for 10-15 minutes before attempting to remove or slice. This allows the cheese and sauce to set, preventing a gooey mess. Slice into wedges and serve hot.