Start cooking the pasta following the package instructions.
In a large ziplock bag, mix together 3 Tsp of Cajun seasoning, ¼ Tsp of salt, and ¼ Tsp of pepper. Add the chopped chicken, seal the bag, and shake until the chicken is well coated. Set it aside.
In a large pan over medium heat, melt 2 Tbsp of butter.
Move the chicken to a heated pan and cook until browned and cooked through, working in batches if necessary. Transfer to a plate and set aside.
Next, add the remaining tablespoon of butter to the pan and let it melt. Add the peppers and onion, stirring frequently until they start to soften, about 5 minutes.
Stir in the heavy cream, smoked paprika, basil, garlic powder, and the remaining Cajun seasoning along with ¼ Tsp of salt and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer until the sauce thickens.
Once thickened, return the cooked chicken to the pan. Add the Parmesan cheese and the warm, drained pasta, stirring until the cheese melts. Serve warm, garnished with fresh parsley if you like.