Bring a large pot of water to a boil. Cook broccoli in boiling water for about 5 minutes. Use a slotted spoon to remove broccoli to a large bowl and set aside.

Season boiling water in the same pot with salt. Cook cavatelli in boiling water until tender yet firm to the bite, 8 to 10 minutes. Drain and set aside.

Heat olive oil in a large skillet over medium heat. Sauté garlic in hot oil until lightly golden, being careful not to burn it. Add broccoli; cook, stirring occasionally, until tender yet crisp to the bite, about 10 minutes.

Add cooked cavatelli to the skillet; toss well with broccoli mixture until warmed through. Season with salt and hot pepper flakes. Serve with Parmesan cheese.