Dissolve the sugar and yeast in warm water in a large bowl; let stand 5 minutes. Lightly spoon flour into dry measuring cups; level with a knife. Add 1 1/4 cups flour and 1/4 teaspoon salt to yeast mixture, and stir until a soft dough forms. Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel tacky).
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, 30 minutes 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. Line a baking sheet with parchment paper; sprinkle with cornmeal. Roll dough into a 12-inch circle on a floured surface. Place dough on prepared baking sheet. Crimp edges of dough with fingers to form a rim; let rise 10 minutes.
Preheat oven to 475°.
While dough rises, heat 2 teaspoons olive oil in a large nonstick skillet over medium heat. Add 1/4 teaspoon salt and mushrooms, and cook 7 minutes or until mushrooms soften and moisture almost evaporates, stirring frequently.
Sprinkle 1/4 cup fontina evenly over dough, and arrange the mushroom mixture evenly over fontina. Sprinkle with thyme; drizzle evenly with truffle oil. Sprinkle remaining fontina and Parmesan cheese evenly over top. Bake at 475° for 15 minutes or until crust is lightly browned. Remove to cutting board, and sprinkle with sea salt. Cut into 8 slices. Serve immediately.