Heat 1 tbsp olive oil in a large pot over medium-high heat (I use my enameled cast iron)
Toss chicken with 1/2 tbsp cajun seasoning. Add to pot in a single layer.
Cook until browned on bottom, about 3 minutes then turn and continue to cook through, about 3 minutes longer. Transfer to a sheet of foil and wrap to keep warm
Heat remaining 1/2 tbsp of olive oil in same pot over on medium-high heat. Add bell peppers and onion and saute until soft (about 5 minutes). Add garlic and remaining 1 tbsp cajun seasoning and saute 1 minute longer
Pour in chicken broth, tomatoes and 1/2 cup heavy cream. Bring mixture to boil and then add pasta
Cook, stirring frequently until pasta is nearly tender, about 10-12 minutes. Add cornstarch and water mixture and cook about 1 minute longer until sauce has started to thicken.
Remove from heat. Toss in remaining 1/4 cup cream, parmesan, parsley, and cooked chicken. Season with salt and pepper to taste.