To prepare dough, dissolve sugar and yeast in warm water in a large bowl; let stand 10 minutes. Lightly spoon flour into dry measuring cups; level with a knife. Add 1 cup flour and salt to the yeast mixture, stirring with a whisk until well combined. Stir in 1 3/4 cups flour, stirring until a dough forms. Turn dough out onto a lightly floured surface. Knead the dough until smooth and elastic (about 8 minutes); add enough of remaining 1/4 cup flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel sticky).
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 hour or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.) Punch dough down; cover and let stand 5 minutes.
Preheat oven to 375°.
To prepare topping, heat a large nonstick skillet over medium-high heat. Remove casings from sausage. Coat pan with cooking spray. Add sausage and onion; cook for 5 minutes or until sausage is browned, stirring to crumble. Drain; set sausage mixture aside.
Return pan to medium-high heat. Add mushrooms; cook 5 minutes or until moisture evaporates, stirring frequently. Remove mushrooms from pan, and set aside.
Return pan to medium heat; add 1 teaspoon olive oil. Add garlic; cook 30 seconds or until lightly browned, stirring constantly. Add tomato paste; cook 1 minute, stirring frequently. Stir in oregano, fennel, and tomato sauce; simmer for 5 minutes or until sauce mixture is slightly thickened.
Coat a 12-inch cast-iron skillet with remaining 1/2 teaspoon oil, and sprinkle cornmeal over oil. Place dough in skillet, gently stretching edges to evenly coat bottom and sides of pan. Sprinkle mozzarella evenly over the bottom of dough; top evenly with sausage mixture and mushrooms. Top mushrooms with sauce mixture; sprinkle Parmesan over sauce. Bake at 375° for 40 minutes or until crust browns and topping is bubbly. Let pizza stand 10 minutes before serving.
You can prepare the dough the night before and let it rise in the refrigerator overnight, if you prefer.