Cook the pasta. Boil the pasta in salted water until al dente, then drain and set it aside. Save about 1 cup of pasta water in case you want to loosen the sauce later.
Season the chicken. Toss the chicken strips with Cajun seasoning, salt, and black pepper. Make sure every piece gets coated so the flavor comes through in every bite.
Sear the chicken. Heat the olive oil in a large skillet over medium-high heat.
Add the chicken and cook for 5 to 7 minutes, stirring occasionally, until browned and cooked through. Transfer it to a plate.
Cook the onions and garlic. Add the butter to the same skillet. Stir in the onion and cook for 3 to 4 minutes until softened, then add the garlic and cook for about 30 seconds.
Add the roasted peppers. Stir in the sliced roasted red peppers and let them warm through for a minute.
Their sweet, smoky flavor helps balance the spice in the Cajun seasoning.
Build the sauce. Pour in the chicken broth and scrape up any browned bits from the bottom of the pan. Add the heavy cream, paprika, and red pepper flakes if using, then let the mixture simmer for 2 to 3 minutes.
Stir in the cheese. Lower the heat and add the Parmesan slowly, stirring until smooth and creamy. If the sauce looks too thick, add a splash of the reserved pasta water.
Combine everything. Return the chicken to the skillet, then add the cooked pasta.
Toss until everything is coated in the sauce and heated through.
Finish and serve. Taste and add more salt if needed. Top with chopped parsley and extra Parmesan before serving.