Cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large bowl, toss the chicken pieces with Cajun seasoning until evenly coated.
In a large skillet, heat the olive oil over medium-high heat. Add the seasoned chicken and cook for about 5-7 minutes, or until browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the onion and bell peppers. Sauté for about 5 minutes until the vegetables are softened. Add the garlic and cook for an additional minute.
Pour in the chicken broth and heavy cream, stirring to combine. Bring the mixture to a simmer.
Add the cooked chicken back into the skillet along with the drained pasta. Stir in the Parmesan cheese until melted and well combined. Season with salt and pepper to taste.
Serve hot, garnished with chopped parsley.