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 pasta cooking water, then drain the pasta and set aside.
While the pasta cooks, melt the butter in a skillet over medium heat, add the minced garlic, and cook until fragrant, about 30 seconds.
Stir in the basil pesto and salt and cook until the mixture starts to bubble, 1–2 minutes.
Pour in the reserved pasta water and stir, cooking until the sauce begins to thicken, about 5 minutes.
Reduce heat to low, add the heavy cream, stir, and simmer until the sauce reduces slightly, about 2–3 minutes.
Add the drained pasta to the skillet and toss to coat evenly with the sauce.
Serve topped with grated Parmesan cheese and fresh basil.