Snap off tough ends of asparagus. Remove scales from stalks with a knife or vegetable peeler, if desired. Cut spears into 1-inch pieces; set aside.
Coat a large nonstick skillet with cooking spray. Place over medium-high heat until hot. Add onion and garlic; saute until tender. Add mushrooms; saute 2 minutes. Add rice and next 8 ingredients, stirring well. Bring to a boil; cover, reduce heat, and simmer 35 minutes. Add asparagus, carrot, zucchini, and parsley. Bring to a boil. Cover, reduce heat, and simmer 15 minutes or until vegetables are crisp-tender. Transfer vegetable mixture to a serving bowl; top with cheese.