Pat the chicken breasts dry and season them generously with Cajun seasoning, salt, and black pepper.

Heat olive oil in a large skillet over medium heat. Sauté the chicken until golden brown and cooked through, about 5 to 7 minutes on each side. Once done, remove the chicken from the pan and set it aside to rest.

Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Drain the pasta, reserving one cup of the pasta water for later use.

In the same skillet used for the chicken, add a bit of butter or olive oil. Sauté the diced onions, minced garlic, and sliced bell peppers until softened and fragrant.

Pour in the heavy cream and stir in the freshly grated Parmesan cheese. Season with additional Cajun seasoning if desired. Let the sauce simmer gently until it thickens slightly, adjusting the consistency by adding the reserved pasta water if necessary.

Slice the cooked chicken into strips and return it to the skillet along with the drained pasta. Toss everything together to coat evenly with the creamy Cajun sauce. Heat through for a couple of minutes, then serve immediately. Garnish with extra Parmesan cheese if desired.