Season the chicken. Place the bite-sized chicken pieces in a bowl and toss with 1 tablespoon of Cajun seasoning until evenly coated.
Brown the chicken. Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the chicken and cook for about 4–5 minutes, turning occasionally, until browned on the outside. Transfer the chicken to a plate.
Sauté the vegetables. Add the diced onion and bell peppers to the same pot. Cook for 3–4 minutes until they begin to soften. Add the minced garlic and cook for another 30 seconds.
Add the pasta and broth. Pour in the chicken broth and add the uncooked penne. Stir well, scraping up any browned bits from the bottom of the pot.
Season and simmer. Add the remaining Cajun seasoning and black pepper. Bring everything to a gentle simmer.
Cook the pasta. Cook for approximately 10–12 minutes, stirring frequently, until the pasta is nearly al dente and most of the liquid has been absorbed.
Add the cream and chicken. Stir in the heavy cream and return the browned chicken to the pot. Continue cooking for 3–5 minutes, or until the chicken is completely cooked and the pasta is tender.
Add Parmesan. Reduce the heat to low and stir in the Parmesan cheese. Continue stirring until the cheese has melted and the sauce is creamy.
Adjust the seasoning. Taste and add salt or additional Cajun seasoning if needed. If the sauce is too thick, add a small splash of chicken broth or cream.
Rest and serve. Remove from the heat and let the pasta rest for 1–2 minutes. Garnish with fresh parsley and sliced green onions before serving.
