Cook ground round in a medium saucepan over medium-high heat until browned, stirring until it crumbles. Drain and pat dry with paper towels. Wipe drippings from pan with a paper towel. Set meat aside.
Coat saucepan with cooking spray; place over medium heat until hot. Add mushrooms, carrot, green pepper, celery, and garlic; saute 3 minutes. Return meat to pan. Add tomato and next 11 ingredients; bring to a boil. Cover, reduce heat, and simmer 20 minutes. Uncover and simmer 20 minutes or until thickened, stirring occasionally. Remove and discard bay leaf. Spoon sauce over spaghetti. Sprinkle with Parmesan cheese.