Bring a large pot of generously salted water to a boil.
Heat oil and 2 tbsp butter in a large deep skillet. Add the andouille sausage and sauté for about 2 minutes. Add shrimp and garlic, then season with garlic powder, onion powder, Cajun seasoning, smoked paprika, salt and pepper. Cook just until the shrimp turn pink. Remove shrimp and sausage and set aside.
Add 1 tbsp butter and diced onion to the same skillet. Sauté for about 5 minutes. Add garlic and cook another 30 seconds.
Pour in heavy cream. Add garlic powder, onion powder, Cajun seasoning, salt and pepper. Bring to a gentle simmer, reduce heat to low and cook for 5–7 minutes, stirring often.
Meanwhile, cook the cavatappi pasta according to package directions. Add the broccoli during the last 3 minutes of cooking. Reserve about 1 cup pasta water, then drain.
Stir ½–¾ cup Parmesan into the cream sauce. Taste and adjust seasoning as needed.
Add the cavatappi and broccoli and toss until coated. Add reserved pasta water a little at a time as needed to loosen the sauce.
Add the shrimp and sausage back to the skillet, toss everything together and serve with extra Parmesan.
