Coat chicken breasts with half the Cajun seasoning (1.5 teaspoons). In a large, heavy-bottomed pot heat olive oil over medium-high heat. Cook the chicken breasts until the internal temperature reaches 165 degrees, roughly 4-5 minutes per side. Remove and set aside.
Add the bell pepper to the pot and saute for 3-4 minutes. Add the garlic and saute for another 60 seconds being careful not to burn the garlic. Remove the peppers and garlic and set aside.
Add the chicken broth, heavy whipping cream, pasta, and remaining Cajun Seasoning (1.5 teaspoons) to the pot. Bring to a boil, cover, and cook for an additional 8-10 minutes, or until the pasta is al dente, stirring once halfway through.
Remove the lid. There should be enough liquid to melt the cheese and still coat all the pasta, about a cup of liquid. Add more chicken broth, cream, or milk, if necessary.
Add the cheese, stir until melted. Stir in the peppers and garlic. Cut the chicken into 1/2 strips against the grain and top the pasta with it. Add salt and pepper to taste. Serve while hot.