In a large mixing bowl, combine warm water, sugar, and active dry yeast. Let sit for 5-10 minutes until frothy.

Add all-purpose flour, yellow cornmeal, salt, melted unsalted butter, and olive oil. Mix until rough dough forms, then knead for 5-7 minutes until smooth and elastic.

Place the dough in a greased bowl, cover, and let rise in a warm area for about 1.5 hours, or until doubled in size.

Heat a skillet over medium heat. Add crumbled Italian sausage and cook until browned, about 6-8 minutes.

Transfer sausage to a plate. In the same skillet, melt unsalted butter and sauté onion, green bell pepper, and minced garlic until soft, about 5 minutes.

In a saucepan, heat olive oil over medium heat. Add crushed tomatoes, dried oregano, dried basil, salt, black pepper, and sugar. Stir and let simmer for 15 minutes.

Preheat your oven to 425°F (220°C). Roll out the dough into a large circle and press into a greased deep-dish pan.

Layer shredded mozzarella cheese, cooked sausage, sautéed vegetables, and spoon the sauce on top, leaving space for a crust.

Bake for 25-30 minutes until crust is golden brown and cheese is bubbly.

Let cool for about 10 minutes before slicing and serving.