1. Dissolve yeast and sugar in 3/4 cup warm water in the bowl of a stand mixer; let stand 5 minutes. Add 3 tablespoons oil. Weigh or lightly spoon 7.9 ounces (about 1 3/4 cups) all-purpose flour into dry measuring cups; level with a knife. Add 7.9 ounces flour, semolina, and 3/8 teaspoon salt to yeast mixture; mix at medium-low speed with a dough hook until smooth (about 4 minutes). Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 5 minutes), gradually adding remaining 1/4 cup all-purpose flour. Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 1/2 hours or until doubled in size.
2. Heat a large skillet over medium-high heat. Add 1 tablespoon oil; swirl to coat. Add onion; cook 3 minutes or just until tender. Stir in garlic; cook 30 seconds, stirring constantly. Add oregano, 1/8 teaspoon salt, pepper, and mushrooms. Cook 6 minutes or until mushrooms release their moisture.
3. Combine remaining 1/8 teaspoon salt, marinara, and bay leaf in a saucepan. Bring to a boil; reduce heat, and simmer 5 minutes. Discard bay leaf.
4. Preheat oven to 425°. Place oven rack in bottom third of oven.
5. Coat bottom and sides of a 10-inch springform pan with 1 tablespoon oil. Punch dough down; turn dough out onto a lightly floured surface. Gently press dough into a 13-inch circle. Carefully lift dough and place in prepared pan. Press dough into bottom and halfway up sides of pan. Sprinkle Parmesan evenly over dough. Top with mushroom mixture. Spread marinara mixture over mushroom mixture. Sprinkle with mozzarella. Bake at 425° for 28 minutes or until crust and cheese are browned. Let stand 5 minutes. Cut into 6 wedges.