Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente, about 10-12 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat.
Toss the chicken pieces with Cajun seasoning until evenly coated.
Add the chicken to the skillet and cook for 5-7 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced red bell pepper, green bell pepper, and onion. Cook for 4-5 minutes until the vegetables are tender.
Add the minced garlic to the skillet and cook for 1 minute until fragrant.
Pour in the heavy cream and chicken broth, stirring to combine. Bring the mixture to a simmer.
Add the grated Parmesan cheese, salt, and black pepper. Stir 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 penne pasta to the skillet and toss everything together until the pasta is well coated with the creamy Cajun sauce.
Cook for an additional 2 minutes to heat through.
Remove from heat and sprinkle with chopped fresh parsley before serving.