Heat 1 Tbsp olive oil in a large pot over medium-high heat.
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 olive oil in same pot over medium-high heat. Add bell peppers and onion and saute 3 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 a boil, then add pasta.
Cook, stirring frequently until pasta is nearly tender, about 12 - 13 minutes. Add cornstarch and water mixture and cook until pasta is just tender and sauce mixture has thickened, about 1 minute longer.
Remove from heat. Toss in remaining 1/4 cup cream, parmesan, parsley and cooked chicken, and season with salt and pepper to taste. Serve warm.