Bring a large pot of water to a boil; add pasta and cook until al dente, about 10 minutes.
Meanwhile, heat the olive oil in a large, nonstick skillet. Add chicken and cook over medium heat until the bottom begins to turn golden. Turn chicken over and cook 1 minute longer.
Stir in garlic, asparagus, scallions, carrots, chicken broth, parsley, and nutmeg. Cover and cook for about 5 minutes, or until chicken is cooked through and vegetables are tender-crisp. Remove from heat.
Stir in roasted pepper and cherry tomatoes. When pasta is cooked, drain and return to pot. Toss with chicken, vegetables, and parmesan cheese over medium heat until heated through. Season with salt and pepper. Serve immediately.