In a large bowl, stir together warm water, yeast, and sugar. Let stand 5 minutes until foamy.
Add flour, cornmeal, salt, melted butter, and olive oil. Mix until a shaggy dough forms, then knead 6 to 8 minutes until smooth.
Place dough in a lightly oiled bowl, cover, and let rise 60 to 90 minutes, until doubled.
While dough rises, make the sauce: heat olive oil in a saucepan, cook garlic 30 seconds, then stir in crushed tomatoes, tomato paste, sugar, oregano, basil, salt, and red pepper flakes. Simmer 15 minutes.
Preheat oven to 425°F. Grease a deep dish pan generously with butter and olive oil.
Punch down dough and roll into a 14-inch circle. Press into the pan, covering the bottom and pushing dough up the sides.
Layer mozzarella across the dough, then add sausage and any cooked toppings. Spoon sauce evenly over the top and finish with Parmesan.
Bake 25 to 35 minutes, until crust is deep golden and filling is bubbling. If needed, tent with foil near the end.
Rest 10 to 15 minutes before slicing and serving.