Wild Mushroom Pizza with Truffle Oil

Name: Wild Mushroom Pizza with Truffle Oil
Ingredients: 1 teaspoon sugar; 1 package quick-rise yeast (about 2 1/4 teaspoons); 1/2 cup warm water (100° to 110°); 1 1/2 cups all-purpose flour, divided; 1/2 teaspoon salt, divided; Cooking spray; 2 teaspoons cornmeal; 2 teaspoons olive oil; 2 cups thinly sliced shiitake mushroom caps (about 4 ounces); 2 cups sliced cremini mushrooms (about 4 ounces); 1 1/2 cups (1/4-inch-thick) slices portobello mushrooms (about 4 ounces); 2.5 ounces shredded fontina cheese (about 2/3 cup), divided; 2 teaspoons chopped fresh thyme; 1/2 teaspoon truffle oil; 1 ounce grated fresh Parmesan cheese (about 1/4 cup); 1/4 teaspoon sea salt or flake salt