Cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium-high heat.
Toss the chicken pieces with Cajun seasoning until evenly coated.
Add the seasoned chicken to the skillet and cook for 5-7 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. Remove chicken from skillet and set aside.
In the same skillet, add the sliced red bell pepper, yellow bell pepper, and onion. Cook for 4-5 minutes until the vegetables are tender.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the heavy cream and chicken broth, stirring to combine.
Bring the sauce to a simmer and cook for 3-4 minutes until slightly thickened.
Stir in the grated Parmesan cheese, salt, and black pepper until the cheese is melted and the sauce is creamy.
Return the cooked chicken to the skillet and stir to coat with the sauce.
Add the cooked pasta to the skillet and toss everything together until well combined and heated through.
Remove from heat and sprinkle with chopped fresh parsley before serving.