1. Cook pasta according to package directions, omitting salt and fat; drain. Keep warm.
2. Heat a large nonstick skillet over medium-high heat. Add beef; cook 2 minutes or until browned, stirring to crumble. Remove beef from pan; set beef aside.
3. Return pan to medium-high heat. Add oil; swirl to coat. Add carrot, onion, and mushrooms; sauté 5 minutes or just until tender. Stir in zucchini, 1/2 teaspoon salt, 1/8 teaspoon black pepper, and garlic; cook 4 minutes or until vegetables are tender, stirring occasionally. Stir in beef; cook 1 minute. Add tomatoes, tomato paste, and crushed red pepper to pan; bring to a boil. Reduce heat to medium-low; cover and simmer 8 minutes or until slightly thickened, stirring occasionally. Stir in cream; cook 1 minute. Remove pan from heat; stir in remaining 1/4 teaspoon salt, remaining 1/8 teaspoon black pepper, and 2 tablespoons Parmesan cheese. Divide pasta among 4 bowls. Top each serving with 1 1/4 cups sauce; sprinkle evenly with remaining 2 tablespoons Parmesan cheese.