Rub each chicken breast with 1 teaspoon of cajun seasoning. Heat a large skillet over medium-high heat. Add in 3 tablespoons of butter. Sear the chicken breasts in the butter until browned on each side. Reduce the heat to medium-low and continue to cook until the chicken reaches an internal temperature of 165 degrees F which will take about 5-7 minutes per side, depending on thickness. Remove the chicken and set aside to rest.
Cook pasta according to package directions.
In the same skillet as you cooked the chicken, without cleaning, melt the remaining 3 tablespoons of butter. Add in bell peppers, onion, and mushroom. Sauté until veggies are tender. Sprinkle remaining 2 teaspoons of cajun seasoning over veggies and cook 1 minute.
Pour in heavy cream and bring to a simmer. Simmer until sauce thickens.
Stir in cooked pasta and toss until coated and veggies are evenly distributed. Slice chicken breasts and serve over hot pasta.