Blanch broccoli for 5 minutes in a large pot of boiling water. Set aside after draining.

In a large skillet over medium heat, heat the olive oil. Cook the garlic until it is lightly golden, taking care not to burn it. Mix in the broccoli. Cook for about 10 minutes, stirring occasionally. Broccoli should be tender but still crunchy to the bite.

Meanwhile, cook cavatelli for 8 to 10 minutes, or until al dente, in a large pot of boiling salted water. Drain and transfer to a large serving bowl. Season with salt and hot pepper flakes and toss with the broccoli. Garnish with parmesan cheese.