Place a large nonstick skillet over medium-high heat. Coat zucchini with cooking spray, and sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add zucchini and garlic to skillet; cook, stirring constantly, 3 minutes or until tender. Set aside, and keep warm.
Wipe skillet clean with paper towels. Coat mushrooms with cooking spray. Place skillet over medium-high heat until hot. Add mushrooms; cook, stirring constantly, 3 minutes or until golden. Stir in wine, green onions, and 1/4 teaspoon salt; cook 2 to 3 minutes or until liquid is absorbed. Set aside, and keep warm.
Wipe skillet clean with paper towels. Sprinkle veal evenly with remaining 1/4 teaspoon salt and remaining 1/4 teaspoon pepper. Coat veal with cooking spray. Place skillet over high heat. Add half of veal, and cook 1 minute on each side or until browned. Repeat procedure with remaining veal. Remove veal from skillet. Set aside; keep warm.
Add water to skillet; cook until liquid is reduced to 1/4 cup, scraping pan to loosen browned bits. Return mushrooms and veal to skillet; toss to coat with sauce. Sprinkle with cheese, and serve with zucchini.