PLACE squash in large saucepan. Cover with water; bring to a boil. Cook over medium-high heat for 30 to 35 minutes or until tender; drain. Place back in saucepan. Mash with a potato masher. Stir in sugar and salt.
MEANWHILE, HEAT vegetable oil in medium skillet over medium-high heat. Add onion, stirring occasionally, for 4 to 5 minutes or until onion is soft and golden.
STIR onions into squash mixture. Add evaporated milk. Cook over medium-high heat, stirring occasionally, until mixture comes to a boil. Reduce heat to medium-low. Gradually stir in corn meal. Continue cooking for 5 minutes or until thickened. Cover saucepan; cook, stirring occasionally, for an additional 5 minutes. Remove from heat. Stir in cheese until blended. Serve immediately.