Season the chicken breasts generously with salt, pepper, and Cajun seasoning. Heat olive oil in a skillet over medium-high heat, add the chicken, and sear for about 6–7 minutes on each side until golden brown and cooked through. Remove and set aside to rest.

Bring a large pot of salted water to a boil. Add pasta and cook per package instructions until al dente, about 8-10 minutes. Reserve 1 cup of pasta water before draining.

In the same skillet, melt butter over medium heat. Add minced garlic and sauté for 1 minute until fragrant. Add more Cajun seasoning and smoked paprika, sauté for another minute, then pour in heavy cream and chicken broth. Let simmer for 4-5 minutes until slightly thickened.

Stir in grated Parmesan cheese until melted. Add drained pasta, tossing to coat in the sauce. Slice the rested chicken and mix it in. If the sauce is too thick, add reserved pasta water to reach desired consistency.

Turn off heat, taste the pasta, and adjust seasoning if needed. Serve with a sprinkle of fresh parsley and additional Parmesan on top.