Cook the pasta according to the package directions in a large pot of salted water until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Once hot, add diced onions and bell peppers, sautéing until soft.
Add the chicken to the skillet, sprinkling Cajun seasoning on top. Cook until the chicken is browned and cooked through, about 7-10 minutes.
Pour in the chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the skillet.
Stir in the heavy cream and Parmesan cheese. Allow the sauce to simmer for about 5 minutes until thickened.
Combine the cooked pasta into the sauce, tossing until well coated. Season with salt and pepper to taste.
Serve hot, garnished with additional Parmesan and fresh herbs if desired.