Cook the rigatoni. Bring a large pot of salted water to a boil. Cook the rigatoni according to package directions until al dente. Reserve about 1/2 cup pasta water, then drain.
Season the chicken. Pat the chicken breasts dry. If they are very thick, slice them horizontally or pound them to an even thickness. Coat both sides with Cajun seasoning, smoked paprika, garlic powder, and black pepper.
Blacken the chicken. Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add the seasoned chicken and cook for about 4–6 minutes per side, depending on thickness, until deeply browned and the center reaches 165°F.
Rest and slice. Transfer the chicken to a cutting board and let it rest for about 5 minutes before slicing into strips.
Sauté the garlic. Reduce the skillet to medium-low heat. Add 2 tablespoons butter and the minced garlic. Cook for about 30–60 seconds, stirring frequently, until fragrant without letting the garlic brown.
Make the Alfredo sauce. Pour in the heavy cream and stir, scraping up the flavorful browned bits from the skillet. Let the cream gently simmer for 2–3 minutes.
Add the Parmesan. Reduce the heat to low and gradually stir in the Parmesan until melted and smooth. Season with black pepper and add salt only if needed.
Combine with rigatoni. Add the drained pasta to the skillet and toss until thoroughly coated. Add reserved pasta water a tablespoon or two at a time if the Alfredo sauce needs thinning.
Finish and serve. Divide the creamy rigatoni between bowls and top with sliced blackened Cajun chicken. Garnish with parsley and extra Parmesan, if desired. Serve immediately.