Instructions

1. Make the dough:
2. In a stand mixer fitted with a paddle attachment, combine 1/2 cup of the warm water, 1/2 teaspoon of the sugar, and the yeast and stir to just combine. Let stand for 3 to 5 minutes, until it bubbles and foams.
3. Meanwhile, in a mixing bowl combine the flour, semolina, salt, and remaining sugar and whisk to combine. Pour the remaining water into the mixer and mix at low speed to combine. Scrape down the paddle attachment and the bottom of the bowl and add the scrapings to the dough. Switch to the kneading hook. Add the flour mixture and oil and mix for 2 minutes, or just until the dough comes together as a uniform mixture.
4. Add the butter to the dough, about 1 tablespoon at a time, mixing for about 20 to 30 seconds after each addition for a total of 2 to 3 minutes, or until the butter is incorporated; scrape down the sides and bottom of the mixer bowl and the dough hook before the last addition. You will have a soft, tacky, not-sticky, loose dough (avoid kneading heavily in order to maintain the light texture that defines most Chicago-style crusts). Transfer to a large mixing bowl. Cover with plastic wrap and a kitchen towel and refrigerate overnight. (Note: You can let this dough rise at room temperature in the kitchen for about 2 hours or until it has expanded to about 1 1/2 times its size, but the taste, texture, and ease of handling are far better when it has a slow, chilly overnight rise.)
5. When you are ready to assemble the pizza, preheat the oven to 425°F.
6. Flatten the dough with water-moistened fingertips, and gently stretch to about 16 inches. Cover loosely with plastic wrap and allow to rest for 10 minutes. Using a pastry brush, liberally spread the canola or vegetable oil around the bottom and sides of a 12- to 14-inch cast-iron skillet. Fit the dough into the skillet, tucking it in and pressing it up the edges of the pan to the very top. It should be about 1/2- to 3/4-inch thick (don't go crazy rolling or yanking, and don't fold it; remember, if you handle it too roughly, you will lose its lovely tenderness).
7. Make the sausage and mushroom topping:
8. Heat the oil and butter in a saucepan set over medium-high until the butter foams and is fully melted. Add the onions and stir well. Cook, stirring occasionally, for 4 to 5 minutes, until the onions are translucent with browned edges. Add the sausage and cook, stirring with a sturdy, heat-resistant spatula to break it up. Cook for 2 to 3 minutes, add the mushrooms, and stir well. Reduce the heat to medium and cook for 10 to 12 minutes, until the mushrooms have softened and released their liquid. Remove from the heat and set aside while you make the sauce.
9. Make the sauce:
10. Heat the oil in a large saucepan set over medium-high until it shimmers. Add the onions and cook, stirring occasionally, for 7 to 8 minutes, or until lightly browned. Add the garlic, stir, and cook for 30 seconds. Turn off the heat. Add the basil, oregano, thyme, rosemary, sugar, salt, white pepper, hot pepper flakes, and tomatoes. Stir and let stand while you put the pizza together.
11. Slice the mozzarella into 1/8-inch slices, patting each slice well with a paper towel.
12. Completely cover the bottom of the crust with the mozzarella, making more than one layer if necessary to use all the cheese.
13. Spoon the sausage and mushroom mixture evenly over the mozzarella and then scatter the ricotta salata and romano cheeses evenly over the surface. Spoon the sauce over it, spreading it evenly. Bake for 30 to 35 minutes, until heated through and the cheese is completely melted. (The dough should register at least 200°F on an instant-read thermometer, but be careful to insert it into the dough, not the filling, to get an accurate reading.) Let the pizza cool for 10 minutes, cut it into wedges, and serve (when you cut it, the liquids of the fillings and sauce will moisten the bottom of the dough). If you wish, pass additional fresh basil and hot pepper flakes at the table.