Heat oven to 375°F. Grease or spray large cookie sheet. Unroll dough into 1 large rectangle on cookie sheet; press into 13x9-inch rectangle, firmly pressing perforations to seal. Fold edges over 1/2 inch to form edges on crust. Bake 9 minutes.
Meanwhile, cut root end off onion, creating flat surface. Place flat surface on cutting board; cut onion in half vertically, and peel off outer layer. Place large flat side down; cut into 1/8-inch slices. In 10-inch skillet, heat oil over medium heat. Add onion and rosemary; cook 8 to 10 minutes, stirring frequently, until onions are caramelized. Stir in brown sugar.
Arrange cheese evenly over partially baked crust; top with onions.
Bake 4 to 6 minutes longer or until crust is golden brown. Cut into 6 rows by 3 rows. Serve warm.