Heat 1 tablespoon oil in a medium skillet over medium heat. Add chicken and saute for 5 to 7 minutes, or until chicken is cooked through (no longer pink). Remove from skillet and drain on paper towels.
Bring a large pot of lightly salted water to a boil. Add pasta and cook for 2 to 4 minutes, or until al dente; drain and set aside.
While pasta is cooking, heat 2nd tablespoon oil over medium heat in same skillet used for chicken. Stir fry carrots for about 4 minutes, then add broccoli and garlic and stir fry for another 2 minutes. Finally, stir in broth, basil and cheese and return chicken to skillet. Reduce heat to low and simmer for about 4 minutes.
Place drained pasta in a large serving bowl. Top with chicken/vegetable mixture and serve immediately.