Cook and drain fettuccine as directed on package; cover to keep warm.
Meanwhile, in 10-inch skillet, heat oil over medium-high heat. Add garlic; cook and stir 30 to 60 seconds or until softened. Stir in chicken, asparagus, carrots and lemon-pepper seasoning. Reserve 1/4 cup of the broth; stir remaining broth into chicken mixture. Heat to boiling. Reduce heat to medium; cover and cook 5 minutes, stirring occasionally, until chicken is thoroughly heated and vegetables are crisp-tender.
In small bowl, blend reserved 1/4 cup broth and the cornstarch until smooth. Add to skillet; cook and stir until thickened. Stir in basil and lemon peel. Spoon chicken mixture over fettuccine; toss to coat. Sprinkle cheese over individual servings.