1. Cook pasta according to package directions, omitting salt and fat; drain and place in a large bowl.
2. While pasta cooks, melt butter in a large nonstick skillet over medium heat. Add carrot, and sauté 1 minute. Add broth, and bring to a simmer; cover and cook 5 minutes. Add green onions; cover and simmer 2 minutes. Uncover and simmer 4 minutes or until almost all liquid is absorbed. Add peas; cook 2 minutes. Remove from heat; add to pasta.
3. Combine half-and-half and cornstarch in a small saucepan over medium-low heat, stirring with a whisk. Bring to a simmer, and cook 2 minutes or until slightly thickened, stirring frequently. Remove from heat; add garlic and next 3 ingredients, stirring until cheese melts. Pour over pasta and vegetables; toss to combine.