In a large pot of boiling water, blanch broccoli for about 5 minutes. Drain, and set aside.
Heat olive oil in a large skillet over medium heat. Saute garlic until lightly golden, being careful not to burn it. Add the broccoli. Saute, stirring occasionally, for about 10 minutes. Broccoli should be tender yet crisp to the bite.
Meanwhile, cook cavatelli in a large pot of boiling salted water for 8 to 10 minutes, or until al dente. Drain, and place in a large serving bowl. Toss with the broccoli, and season with salt and hot pepper flakes. Serve with parmesan cheese.