Add warm water to combined yeast and sugar in large bowl; stir. Let stand 5 min. Stir in 3 cups flour and 3 Tbsp. oil until mixture is well blended and forms soft dough. Place on work surface sprinkled with remaining flour. Knead dough until smooth and elastic; shape into ball. Place in separate large bowl brushed with 1 Tbsp. oil; turn dough over. Cover with plastic wrap. Let rise in warm place 1 hour or until doubled in volume.
Meanwhile, cook onions and sugar in remaining oil in medium skillet on medium-low heat 10 to 12 min. or until onions are caramelized, stirring occasionally. Add mushrooms; cook 5 min., stirring occasionally.
Heat oven to 450 degrees F. Spray baking sheet with cooking spray; sprinkle with cornmeal. Pat dough into 13x9-inch rectangle on prepared baking sheet. Bake 5 min. Spread with cooking creme; top with vegetable mixture, rosemary and shredded cheese.
Bake 10 to 12 min. or until crust is golden brown and cheese is melted.