Start heating a large pot of salted water for pasta. While it comes to a boil, prep your other ingredients. Once boiling, cook the pasta according to package directions until al dente (usually 8-10 minutes). Before draining, reserve 1/2 cup of the starchy pasta water. Drain and set aside.

While pasta cooks, season the chicken pieces generously with Cajun seasoning, salt, and pepper on all sides.

Heat olive oil and butter in a large skillet over medium-high heat until the butter melts and starts to sizzle. Add the seasoned chicken in a single layer and cook without moving for 2-3 minutes until golden brown underneath, then flip and cook another 2-3 minutes until cooked through (internal temperature should reach 165°F). Remove chicken to a plate.

In the same skillet, add the bell pepper and onion. Cook for 4-5 minutes, stirring occasionally, until the vegetables soften and the onion becomes translucent. Add the minced garlic and cook for 1 minute until fragrant but not browned.

Reduce heat to medium-low and pour in the heavy cream and chicken broth. Let it simmer gently for 3-4 minutes, stirring occasionally, until the sauce thickens slightly and reduces by about one-third.

Stir in the Parmesan cheese until completely melted and the sauce becomes smooth and glossy. Return the cooked chicken to the skillet along with any accumulated juices and toss to coat everything in the sauce.

Add the cooked pasta to the skillet and toss everything together until the pasta is completely coated. If the sauce seems too thick, add reserved pasta water a tablespoon at a time until you reach the right consistency. Garnish with fresh parsley and serve immediately.