Coat chicken with olive oil. Then generously coat with cajun seasoning. Heat up iron skillet medium high heat. When hot add a couple of tablespoons of olive oil to pan. When it's almost smoking add chicken. Cook on one side until the chicken is black then flip and cook until black as well. Once chicken is blackened turn heat down to medium low and continue to cook until done. About 5-10 minutes depending on how thick your chicken breast are. Let rest while cooking sauce. Slice before serving on top of pasta.
In a sauce pan melt your butter. Add garlic and cook for about 1 min. Once you really start smelling that garlic it's done. Don't burn the garlic it taste bad. Now add the flour and mix well cooking for another minute or so. Add your chicken broth and heavy cream. Cook until sauce boils and thickens stirring frequently. Add cheese and season with salt and pepper to taste. Stir until cheese is melted. Add pasta and let simmer for a few minutes to finish cooking that pasta and this lets the sauce adhere better to the pasta.