Bring a large pot of salted water to a boil. Add the cavatappi pasta and cook according to package instructions until al dente, usually about 8-10 minutes. Reserve about 1/2 cup of pasta water, then drain the pasta in a colander and set aside.
In a skillet, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes.
Stir in the minced garlic and sliced mushrooms. Cook for another 5-7 minutes, stirring occasionally, until the mushrooms are tender and have released their moisture.
Pour in the vegetable broth and bring the mixture to a simmer. Then reduce the heat and stir in the heavy cream, allowing it to thicken for about 3-4 minutes.
Add the grated Parmesan cheese and stir until melted and combined. Season with salt and black pepper to taste.
Add the cooked cavatappi to the skillet with the sauce. Toss everything together, adding reserved pasta water if necessary to reach desired sauce consistency.
Serve immediately, garnished with chopped fresh parsley.