In a large pot, bring salted water to a rapid boil. Add the penne pasta and cook according to the package instructions until al dente (usually around 10-12 minutes). Drain the pasta and set it aside, reserving a cup of the pasta cooking water for later use.
Heat olive oil in a large, deep skillet over medium-high heat. Season the chicken pieces generously with Cajun seasoning, salt, and pepper. Once the oil is hot, add the seasoned chicken to the skillet. Cook for 5-7 minutes, stirring occasionally, until the chicken is golden brown and fully cooked. Remove the chicken from the skillet and set it aside on a plate.
In the same skillet, add the sliced bell pepper and diced onion. Sauté for 3-4 minutes until the vegetables soften and start to become fragrant. Incorporate the minced garlic and continue cooking for an additional minute until the garlic is aromatic but not burned.
Lower the heat to medium and pour the chicken broth and heavy cream into the skillet. Use a wooden spoon or spatula to stir and combine, scraping up any browned bits from the bottom of the skillet. Allow the mixture to come to a gentle simmer and cook for about 3-4 minutes, or until the sauce begins to thicken.
Return the sautéed chicken to the skillet and gently fold in the cooked penne pasta. Sprinkle in the grated Parmesan cheese and stir until everything is evenly coated in the creamy sauce. If the sauce seems too thick, add a bit of the reserved pasta water to reach your desired consistency. Taste and adjust the seasoning with additional salt and pepper if necessary.
Once everything is well mixed and heated through, remove from heat. Transfer the creamy Cajun chicken penne to serving bowls and garnish with freshly chopped parsley.
Notes
Serve in wide, shallow bowls and top with extra grated Parmesan and Cajun seasoning for added flavor.