Bring a large pot of water to a boil. Season liberally with salt. Cook pasta according to package directions until al dente. Drain and set aside.
While the pasta cooks, place a large skillet over medium-high heat and add 2 tablespoons olive oil to the pan.
In a small bowl, combine the Cajun seasoning ingredients. Cut each chicken breast into 3 pieces, which each piece about the same size and thickness. Season the chicken on both sides with the Cajun seasoning. Place chicken in the hot pan and cook for 6 to 8 minutes, turning once, until the chicken is cooked through and no longer pink. Transfer to a cutting board to rest.
To the same skillet add the remaining olive oil, bell peppers, and onion. Cook for about 5 minutes, or until the veggies have softened and the onions are translucent. Add garlic and cook for another 2 minutes.
Sprinkle the flour over the veggies and stir to coat. Cook for 1 minute. Pour the milk into the skillet and stir to combine the flour and milk. Add the cream and hot sauce; stir again. Cook for 5 to 7 minutes or until the sauce is bubbling and thickened, stirring often. Season liberally with salt and pepper to taste.
Add the pasta to the skillet and toss to coat the pasta in sauce. Transfer the pasta to a serving bowl. Slice the chicken breasts and place on top of the pasta. Garnish with lots of parsley. Serve immediately.