In a saucepan, heat the olive oil over moderate heat until hot. Add the garlic and cook it, stirring, until pale golden. Add the broccoli, salt, and red pepper flakes and cook, stirring, for 2 minutes. Add the chicken broth and simmer for 5 minutes.
Meanwhile, cook the pasta. Drain the pasta and transfer it to the saucepan. Toss with sauce to combine. Serve with the cheese.