Pat the chicken breasts dry with a paper towel and coat each breast generously with Cajun seasoning on both sides.
Heat olive oil and butter in a large skillet over medium-high heat. Sear the seasoned chicken breasts for about 4–5 minutes on each side until cooked through. Let rest before slicing.
Bring a large pot of salted water to boil. Add pasta and cook according to package instructions until al dente. Reserve some pasta water before draining.
In the same skillet, melt two tablespoons of butter, add minced garlic and sauté until fragrant. Sprinkle in flour while whisking to form a roux.
Gradually pour in heavy cream while whisking. Stir in smoked paprika, salt, and pepper. Simmer for 2-3 minutes until thickened.
Stir in parmesan cheese until melted and smooth. Adjust sauce consistency with reserved pasta water if needed.
Toss the cooked pasta and sliced chicken into the skillet with the sauce. Mix well and garnish with parsley and extra parmesan before serving.