In large dutch oven, cook pasta as directed on package. Drain, rinse, and set aside.
Heat one tbsp of oil in dutch oven over medium heat. Add peppers, onion, garlic, and cajun seasoning, cook until browned. Add diced tomatoes and cook for 3-5 minutes, or until tomatoes have broken down and peppers are tender. Remove from pan and set aside.
Over medium heat, add olive oil to dutch oven. While oil is heating, pat chicken dry and season with salt and pepper. Brown on both sides. Add broth to pan, scraping lightly to remove any browned bits. Cover and cook for 7 minutes, or until chicken reaches an internal temperature of 165. Transfer to a cutting board and dice chicken.
Melt butter in dutch oven. Stir in flour. Add heavy cream, parmesan cheese, salt, and pepper. Add noodles, vegetables, and chicken back to pan. Toss to coat with sauce.
Garnish with parmesan, fresh parsley, and a sprinkle of cajun seasoning.