Cook the jumbo pasta shells according to package instructions.
Preheat your oven to 375°F (190°C).
In a large mixing bowl, combine the shredded chicken, cream cheese, Monterey Jack cheese, Cajun seasoning, diced tomatoes, and green onions.
Stuff each cooked pasta shell with the chicken mixture.
In a saucepan, combine heavy cream and any remaining Cajun seasoning, heating gently.
Pour the cream mixture into a baking dish and arrange the stuffed shells on top.
Sprinkle grated Parmesan cheese on top.
Cover with foil and bake for 25 minutes, then uncover and bake for an additional 10 to 15 minutes until bubbly and golden.
Let the dish rest for 5 minutes before serving.