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Bring a large pot of salted water to a rolling boil over high heat.
Add the cavatappi pasta and cook until al dente, about 9–11 minutes, reserving 1 cup of pasta water before draining.
Meanwhile, heat the olive oil in a large skillet or Dutch oven over medium-high heat.
Add the ground Italian sausage and cook, breaking it up with a spoon, until browned and no pink remains, about 6–8 minutes.
Drain excess grease, leaving about 1 tablespoon of drippings in the pan.
Reduce heat to medium and add the chopped yellow onion, cooking until translucent, about 5–7 minutes.
Stir in the minced garlic and cook until fragrant, about 1 minute.
Pour in the crushed tomatoes and chicken broth, stir to combine, and bring to a gentle simmer.
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 until the sauce is smooth and warmed through, about 2–3 minutes.
Add the drained pasta to the sauce and toss to coat, adding reserved pasta water as needed to reach desired consistency.
Stir in the chopped fresh basil and serve immediately with extra Parmesan cheese if desired.