In a large pot, bring salted water to a boil. Add the pasta and cook according to package instructions until al dente. Drain and set aside.
While the pasta cooks, season the sliced chicken breasts with Cajun seasoning, salt, and pepper.
In a large skillet, heat the olive oil over medium-high heat. Add the seasoned chicken slices and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and sliced bell peppers. Sauté for about 3-4 minutes until they are tender. Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Pour in the chicken broth and scrape any browned bits from the bottom of the skillet. Let it simmer for 2-3 minutes. Then, add the heavy cream and bring it to a gentle boil.
Stir in the cooked pasta and chicken, then add grated Parmesan cheese. Mix until the pasta is coated in the creamy sauce. Adjust seasoning with salt and pepper as desired.
Remove from heat, garnish with fresh parsley, and serve hot.