Begin cooking pasta according to package instructions.
In a large ziploc bag, toss together 3 teaspoons Cajun seasoning, ¼ teaspoon salt, and ¼ teaspoon pepper. Add chopped chicken, zip closed, and shake until chicken is coated. Set aside.
In a large pan over medium heat, melt 2 Tablespoons of butter.
Transfer chicken to heated pan and cook until chicken is browned and just cooked through (cook in batches if needed). Remove to a plate and set aside.
Add remaining Tablespoon of butter to pan and cook until melted.
Add peppers and onion and cook, stirring frequently until beginning to soften (about 3-5 minutes).
Add heavy cream, smoked paprika, basil, garlic powder, remaining 1 teaspoon of cajun seasoning and ¼ teaspoon salt and pepper. Bring to a boil and then reduce to a simmer, cooking until sauce is thickened.
Return cooked chicken to the pan. Add parmesan cheese and warm cooked, drained pasta and stir until cheese is melted. Serve warm, topped with fresh parsley if desired.