Deep-Dish Mushroom and Onion Pizza

Marinara, mushrooms and sauteed onions make this deep-fried cheese pie truly delicious.
Dissolve yeast and sugar in 3/4 cup warm water in the bowl of a stand mixer; let stand for 5 minutes. Add 3 tablespoons of butter. Spread or lightly spoon 9 ounces (about 1 3/4 cups) of all-purpose flour into dry measuring cups; smooth with a knife. Add 9 ounces of flour, semolina, and 3/8 teaspoon salt to the yeast mixture; beat on medium-low speed with a dough hook until smooth (about 4 minutes). Place the dough on a lightly floured surface. Knead until smooth (about 5 minutes), gradually adding the remaining 1/4 cup all-purpose flour. Place the dough in a large bowl greased with cooking spray, turning it over so that it covers the top. Cover and let rise in a warm place (85 °), draughty, for 1 1/2 hours or until the dough is doubled in size.Preheat a large skillet over medium-high heat. Add 1 tablespoon butter; whisk to coat. Add the onion; cook for 3 minutes or just until tender. Add the garlic; cook for 30 seconds, stirring constantly. Add oregano, 1/8 teaspoon salt, pepper and mushrooms. Cook for 6 minutes or until the mushrooms release moisture.Combine the remaining 1/8 teaspoon salt, marinara and bay leaf in a saucepan. Bring to a boil; reduce heat and simmer 5 minutes. Discard the bay leaf.Preheat the oven to 425 degrees. Place the roasting rack in the bottom third of the oven.Brush the bottom and sides of a 10-inch springform pan with 1 tablespoon of oil. Knead the dough; place the dough on a lightly floured surface. Carefully squeeze a 13-inch circle out of the dough. Carefully lift the dough and place it on the prepared pan. Squeeze the dough out onto the bottom of the pan and half of the sides. Sprinkle the parmesan cheese evenly over the dough. Top with the mushroom mixture. Spread the marinara mixture on top of the mushroom mixture. Sprinkle with mozzarella. Bake at 425 ° C for 28 minutes or until the crust and cheese are lightly browned. Let stand for 5 minutes. Cut into 6 slices.