Bring a large pot of salted water to a boil. Cook the cavatappi according to package instructions until al dente. Drain and set aside.
In a bowl, toss the shrimp with paprika, garlic powder, onion powder, cayenne, thyme, oregano, salt, and pepper until evenly coated.
In a large skillet over medium-high heat, add olive oil. Sear the shrimp for about 1–2 minutes per side, until blackened and cooked through. Remove shrimp from the skillet and set aside.
In the same skillet, melt the butter. Add the minced garlic and sauté for about 30 seconds until fragrant. Stir in the heavy cream and chicken broth. Bring to a simmer, then reduce heat and stir in Parmesan and mozzarella until melted and smooth.
Add the cooked pasta to the sauce, tossing to coat. Stir in the shrimp gently. Season with additional salt and pepper if needed.
Plate the pasta and shrimp. Garnish with chopped parsley or basil if desired. Serve immediately while warm and creamy.