In a large saucepan, bring broth to a boil. Stir in pasta; return to a boil. Reduce heat; simmer, covered, 8 to 10 minutes or until pasta is tender, stirring occasionally.
Meanwhile, in a large skillet, heat oil over medium-high heat. Add chicken and green onions; cook and stir 5 minutes. Add asparagus, mushrooms and garlic; cook and stir 2 to 3 minutes or until chicken is no longer pink and asparagus is crisp-tender. Sprinkle with pepper.
Add chicken mixture to pasta mixture; heat through. Sprinkle with cheese.