Place chicken in a saucepan, and add water to cover. Boil 20 minutes. Allow to cool, then pull meat into shreds.

Bring a large pot of lightly salted water to a boil. Add pasta, and cook for 8 to 10 minutes, or until al dente; drain.

In a large skillet over medium-high heat, combine chicken broth, red pepper, garlic, broccoli, salt and pepper. Cover, and simmer for 8 to 10 minutes, until broccoli is crisp-tender. Stir in cream cheese until smooth. Mix in chicken and pasta until evenly coated. Garnish with Parmesan cheese.