Cook the penne pasta according to package instructions until al dente. Drain and set aside.
While the pasta is cooking, season the chicken breasts with Cajun seasoning, salt, and black pepper.
In a large skillet, heat the olive oil over medium-high heat. Add the seasoned chicken and cook for 5-7 minutes per side until fully cooked. Remove the chicken from the skillet and let it rest before slicing it into strips.
In the same skillet, add diced onion and bell peppers. Sauté until they begin to soften, about 3-5 minutes.
Add the minced garlic and cook for an additional 1 minute until fragrant.
Pour in the chicken broth and bring to a simmer. Reduce heat to low and stir in the heavy cream. Cook for about 2-3 minutes, stirring frequently.
Gradually add the shredded Parmesan cheese, stirring until the sauce is smooth and creamy.
Add the cooked pasta and sliced chicken to the skillet. Stir until all ingredients are well combined and coated with the creamy sauce. Cook for an additional 2 minutes to heat through.
Remove from heat, sprinkle with fresh parsley, and serve immediately.