Cook the penne in salted water until al dente. Reserve 1/2 cup pasta water, then drain.
Pat the chicken dry and season with Cajun seasoning and smoked paprika.
Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat.
Cook the chicken until golden and the internal temperature reaches 165°F (74°C). Transfer to a plate and rest before slicing.
Add the remaining butter to the skillet. Cook the onion and bell peppers for 4–5 minutes.
Add the garlic and cook for approximately 30 seconds.
Pour in the chicken broth and scrape the browned bits from the skillet.
Add the heavy cream and Cajun seasoning and bring to a gentle simmer.
Reduce the heat and gradually stir in the Parmesan until smooth.
Add the cooked penne and toss until coated. Use reserved pasta water to adjust the consistency if necessary.
Add the sliced chicken and finish with parsley, Parmesan and black pepper before serving.