Heat 1 teaspoon oil in large, heavy skillet over medium heat until hot. Brown half of veal; remove from skillet. Repeat with remaining veal. Season with 1/4 teaspoon salt.
Add onion and bell pepper to skillet; cook and stir over medium-high heat 3 to 5 minutes or until tender, stirring frequently. Add mushrooms, prosciutto, wine, if desired, and garlic; cook 1 to 3 minutes or until mushrooms start to brown, stirring occasionally.
Return veal to skillet. Stir in tomatoes, broth, oregano, tomato paste and bay leaves; bring to a boil. Reduce heat; cover tightly and simmer 30 to 45 minutes or until veal is fork-tender.
Meanwhile, preheat oven to 400°F. Line large baking sheet with aluminum foil. Scoop out and discard seeds from each squash half. Rub remaining 2 teaspoons oil over cut surfaces of squash; season with remaining 1/4 teaspoon salt and ground black pepper. Place squash, cut-sides down, on prepared baking sheet. Roast in 400°F oven 45 to 50 minutes or until squash is tender and starts to brown.
Scrape squash flesh into strands with fork; place in large bowl. Add 2 tablespoons cheese; toss.
Divide squash among 4 pasta bowls. Remove and discard bay leaves from veal mixture; ladle evenly over squash. Sprinkle with remaining 2 tablespoons cheese.
Nutrition information per serving: 406 calories; 16 g fat (5 g saturated fat; 6 g monounsaturated fat); 140 mg cholesterol; 1086 mg sodium; 26 g carbohydrate; 4.1 g fiber; 40 g protein; 10.5 mg niacin; 0.6 mg vitamin B6; 1.8 mcg vitamin B12; 2.8 mg iron; 17.5 mcg selenium; 6.0 mg zinc; 145.8 mg choline.