Cook the Pasta: Bring a large pot of salt water to boil. Add the pasta and cook it according to the package instructions until it is firm but tender. Drain the water and set the pasta aside.
Get the chicken ready: Place the chicken pieces in a large, zippered bag. Add the Cajun seasoning, black pepper, and salt. Close the bag tightly and shake it to mix everything and coat the chicken evenly. Heat a big skillet on medium-high heat and add 2 tablespoons of butter. Once the butter is melted and bubbling, add the chicken in a single layer. Cook for 5-7 minutes, flipping it halfway through, until the chicken is golden brown and fully cooked. Take the chicken out of the skillet and set it aside.
Cook the Veggies: In the same skillet, add 1 tablespoon of butter. Turn the heat down a little and toss in the bell peppers and onion. Stir to mix them with the melted butter. Cook for about 5 minutes, or until the peppers and onions start to soften.
Make the Cajun Sauce: Add the extra Cajun seasoning, smoked paprika, dried basil, garlic powder, black pepper, and salt. Stir for about 30 seconds to bring out the flavors of the spices. Slowly pour in the heavy cream, stirring constantly to keep the sauce smooth. Let it simmer for 2-3 minutes until it thickens a little.
Bring It All Together: Add the grated Parmesan cheese to the sauce and stir until it melts. Then, return the cooked chicken (along with any juices from the plate) to the skillet. Finally, add the cooked pasta and stir everything together so it’s all coated in the rich Cajun sauce.
Garnish and Serve: Top with a sprinkle of Parmesan cheese and a little fresh or dried parsley for a burst of color.