Fill a large pot with water, add a pinch of salt, and bring to a rolling boil over high heat.
Add the cavatappi pasta and cook until al dente (9–11 minutes), then reserve 1 cup of pasta cooking water and drain the pasta.
Heat olive oil in a large skillet or Dutch oven over medium-high heat, add the ground Italian sausage, break it up with a spoon, and brown for 6–8 minutes until no pink remains. Drain excess grease, leaving about 1 tablespoon of drippings in the pan, and transfer the sausage to a plate.
Reduce heat to medium, add the chopped yellow onion and cook until softened and translucent (5–7 minutes).
Stir in the minced garlic and cook for 1 minute, until fragrant.
Pour in the crushed tomatoes and chicken broth; stir, bring to a gentle simmer, then reduce heat to low, cover, and simmer for 10 minutes.
Uncover and stir in the heavy cream, grated Parmesan cheese, salt, and black pepper. Cook for 2–3 minutes, stirring occasionally, until the sauce is smooth and creamy.
Add the cooked cavatappi to the sauce and toss until well coated. If the sauce is too thick, add splashes of the reserved pasta water to reach the desired consistency.
Stir in the chopped fresh basil and serve immediately, topped with extra Parmesan cheese.