In a large bowl, whisk together flour, cornmeal, salt, yeast, and sugar. Make a well in center; add ⅔ cup (160 grams) hot water, 1 tablespoon (14 grams) oil, and melted butter. Using a spatula or wooden spoon, stir until a shaggy dough forms, using your hands to bring together if needed.

Turn out dough onto a heavily floured surface. Using floured hands, flatten dough to about 1-inch thickness. Fold dough in half toward you; using heels of your hands, push dough away. Rotate dough 90 degrees, and repeat flattening, folding, pushing, and rotating until dough is lightly tacky and elastic, becomes smoother (dough will not be completely smooth because of the texture from the cornmeal), and passes the windowpane test (see Note), about 12 minutes, lightly flouring work surface and hands as needed.

Lightly oil a large bowl. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 30 to 45 minutes.

In a medium saucepan, heat remaining 1 tablespoon (14 grams) oil over medium-high heat. Add mushrooms, onion, and bell pepper. Cook, stirring occasionally, until softened, onion is translucent, and all water has evaporated, 10 to 15 minutes. Transfer to a medium heatproof bowl, and let cool until ready to use.

Preheat oven to 450°F (230°C). Spread room temperature butter in bottom and up sides of a Lodge 10¼-inch Seasoned Cast Iron Baker's Skillet.

Punch down dough. On a lightly floured surface, roll or stretch dough into a 13-inch circle. Transfer to prepared skillet, pressing into bottom and up sides, making sure dough is even and there are no air bubbles under dough. Sprinkle mozzarella and provolone onto dough in an even layer. Top with sautéed vegetables. Top with sausage and pepperoni. Spoon Pizza Sauce on top, spreading into an even layer.

Bake until crust is golden and an instant-read thermometer inserted in center registers at least 160°F (71°C), 25 to 30 minutes, covering with foil after 20 minutes of baking to prevent excess browning. Top with Parmesan. Let cool for 10 to 15 minutes. Slice and serve from skillet, or remove from skillet, and slice to serve.