Combine ingredients for Cajun seasoning in a small bowl. Or, alternatively, use 2 tablespoons of your favorite Cajun seasoning. My recommendation is Frontier Cajun seasoning.
Place 2 chicken breasts in a shallow bowl and coat on both sides with ½ of the Cajun seasoning. Save the remaining ½ of the seasoning for pasta. Note: be sure to use thinly sliced chicken breasts. That means if you bought large chicken breasts, slice each one in half horizontally.
Heat 2 tablespoons of olive oil in a large skillet on medium-high heat. Add the chicken breasts seasoned with Cajun spice and cook for about 4 minutes on each side. Turn off the heat, cover the skillet with the lid, and let the chicken sit, covered, off heat for about 10 minutes until it's completely cooked through. Remove the chicken to a plate and slice chicken thinly.
In the meantime, bring a large pot of water to boil. Add pasta and cook according to the package instructions (that usually means somewhere between 10 or 15 minutes). Drain pasta.
Add diced bell peppers to the same, now empty, skillet that you just used to cook chicken. Cook on medium heat for about 4 minutes until bell peppers are slightly softened. Remove ½ of the cooked bell peppers to a plate, leaving the remaing ½ in the skillet.
To the same skillet with ½ of the cooked bell peppers, add the cream, the remaining ½ of the Cajun seasoning, and freshly shredded Parmesan cheese. Bring to a brief boil, reduce to simmer, and cook, constantly stirring, until the cheese starts to melt, for several minutes.
Add drained cooked pasta to the skillet with the cream sauce and heat through on low heat. Season with red pepper flakes, more salt and extra cayenne pepper, if desired. Top with sliced cooked chicken and the remaining ½ of cooked bell peppers.