In a skillet, fry sausage over medium heat until no longer pink; drain, and reserve.
In the same skillet, cook garlic in olive oil until golden.
Meanwhile, bring a large pot of lightly salted water to a boil. Cook pasta in boiling water for 8 to 10 minutes or until done; drain. Three minutes before the end of the cooking time, add broccoli; drain with pasta.
In a large serving bowl, toss together the sausage, olive oil and garlic, cavatelli and broccoli, and Parmesan. Season with red pepper flakes.
