Bring a large pot of salted water to a boil. Add the cavatelli pasta and cook according to the package instructions until al dente.

While the pasta cooks, heat the olive oil in a large skillet over medium heat. Add the minced garlic and sauté until fragrant, about 1 minute, being careful not to burn it.

Add the broccoli florets to the skillet and sauté until they are bright green and tender, about 5-7 minutes. Sprinkle with red pepper flakes and salt to taste.

Drain the pasta, reserving 1/2 cup of the pasta water. Add the drained pasta to the skillet with the broccoli. Toss to combine, adding a little pasta water if the mixture seems dry.

Sprinkle with grated Parmesan cheese and toss again until the pasta is well coated and creamy.

Serve hot, with additional Parmesan cheese on the side if desired.