While the dough is rising, make the tomato sauce. In a medium saucepan, heat the oil over medium-high heat. Add the garlic and cook, stirring, for 30 seconds. Add the herbs, seeds, salt, and black and red peppers, and cook, stirring, for 30 seconds. Add the tomatoes, wine and sugar, and bring to a boil. Lower the heat and simmer, stirring occasionally, until thickened, 20 to 30 minutes. Remove from the heat and let cool completely before using.
Preheat the oven to 475 degrees F.
Oil 2 seasoned 12-inch round deep-dish pizza pans with the extra-virgin olive oil. Press 1 piece of dough into each pan, pressing to the edge and stretching about 1 1/2 inches up the sides. Let rest for 5 minutes.
Layer the mozzarella cheese all over the bottom of the pies. Top each with half of the pepperoni, mushrooms, bell pepper rings, onions, black olives and sausage. Ladle the sauce evenly over each pizza and top with Parmesan.
Bake until the top is golden and the cheese is bubbly and the crust is golden brown, about 30 minutes. Remove from the oven, slice and serve hot.
Chicago-style Deep Dish Pizza Dough:
In a large bowl, combine the water, yeast, and sugar and stir to combine. Let sit until the mixture is foamy, about 5 minutes.
Add 1 1/2 cups of the flour, the semolina, 1/2 cup of the oil, and the salt, mixing by hand until it is all incorporated and the mixture is smooth. Continue adding the flour, 1/4 cup at a time, working the dough after each addition, until all the flour is incorporated but the dough is still slightly sticky.
Turn the dough out onto a lightly floured surface and knead until smooth but still slightly tacky, 3 to 5 minutes. Oil a large mixing bowl with the remaining 2 teaspoons oil.
Place the dough in the bowl and turn to oil all sides. Cover the bowl with plastic wrap and set in a warm, draft-free place until nearly doubled in size, 1 to 1 1/2 hours.