Bring a large pot of salted water to a rapid boil, then add the cavatappi and cook until al dente according to package directions.
Before draining, reserve 1/2 cup of the hot pasta cooking water, then drain the pasta and set aside.
While the pasta cooks, melt the butter in a large skillet over medium heat, then add the minced garlic and cook until fragrant, about 30 seconds.
Stir in the basil pesto and salt and cook, stirring, until the mixture begins to bubble, about 1–2 minutes.
Pour in the reserved 1/2 cup pasta water and cook, stirring, until the sauce starts to thicken, about 3–5 minutes.
Reduce heat to low, add the heavy cream, and simmer until slightly reduced, about 2–3 minutes.
Add the drained pasta to the skillet and toss thoroughly to coat with the sauce, adding a splash more pasta water if needed to loosen the sauce.
Serve immediately topped with grated Parmesan and torn fresh basil.
