Pat chicken pieces dry with paper towels. In a medium bowl, toss chicken with 1 tablespoon of olive oil and 2 tablespoons of Cajun seasoning until evenly coated. Chop onion and bell peppers, and mince garlic.

Bring a large pot of salted water to a rolling boil. Add pasta and cook according to package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta.

While the pasta cooks, heat 1 tablespoon of olive oil in a large skillet or Dutch oven over medium-high heat. Add the seasoned chicken in a single layer, ensuring not to overcrowd the pan. Cook for 4-6 minutes, flipping halfway through, until browned and cooked through. Remove chicken from the skillet and set aside.

Reduce heat to medium. Add chopped onion and bell peppers to the same skillet (add a splash of olive oil if needed). Sauté for 5-7 minutes, until softened. Add the minced garlic and the remaining 1 tablespoon of Cajun seasoning. Cook for another minute until fragrant.

Pour in the chicken broth, scraping up any browned bits from the bottom of the pan. Bring to a simmer, then stir in the heavy cream. Let the sauce simmer gently for 3-5 minutes, stirring occasionally, until it begins to thicken slightly.

Stir in the 1/2 cup of Parmesan cheese until melted and smooth. Season with salt and black pepper to taste. If the sauce is too thick, add a splash of reserved pasta water until desired consistency is reached.

Add the cooked chicken back into the skillet with the sauce. Add the drained pasta and toss gently to coat everything evenly. Cook for 1-2 minutes more to allow the flavors to meld.

Garnish with fresh chopped parsley and additional grated Parmesan cheese, if desired. Serve immediately and enjoy!