Cook pasta according to package directions, omitting salt and fat; drain and place in a large bowl.
While pasta cooks, melt butter in a large nonstick skillet over medium heat.
Add carrot, and saut 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.
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.