Boil salted water. Cook pasta until al dente. Reserve ½ cup pasta water. Drain.
Season chicken with 2 tablespoons Cajun seasoning, salt, and pepper.
Heat olive oil in large skillet over medium-high heat.
Add chicken. Cook 5 to 7 minutes until cooked through and browned.
Remove chicken. Set aside.
Melt butter in same skillet over medium heat.
Add bell peppers and onion. Sauté 4 to 5 minutes until tender-crisp.
Add garlic. Cook 30 seconds.
Pour in heavy cream and chicken broth. Stir.
Add 1 tablespoon Cajun seasoning and paprika. Stir well.
Simmer 3 to 4 minutes until sauce thickens slightly.
Reduce to low. Stir in Parmesan until melted and smooth.
Taste. Adjust seasoning as needed.
Return chicken to skillet. Toss to coat.
Add pasta. Toss until well coated.
Add pasta water if sauce is too thick.
Remove from heat. Garnish with parsley, Parmesan, and red pepper flakes.
Serve hot immediately.