Cook Pasta Shells: Boil the pasta shells according to the package instructions. Once cooked, drain and set them aside individually on a tray to cool.
Make the Cajun Cream Sauce: In a medium saucepan, melt the butter over medium heat. Add the chopped garlic and sauté for 1 minute, until fragrant. Stir in the cream (or milk), Parmesan, and Cajun seasoning. Bring to a gentle boil, then reduce heat and simmer for 5 minutes, stirring occasionally.
Prepare Filling: In a large mixing bowl, combine ricotta, cooked chicken, broccoli, green onions, extra Parmesan, lemon zest, and additional Cajun seasoning. Mix until everything is well combined.
Assemble the Dish: Pour the Cajun Alfredo sauce into the bottom of a large baking dish. Stuff each cooled pasta shell with the chicken and broccoli filling. Arrange the stuffed shells on top of the sauce in the baking dish.
Top and Bake: Sprinkle shredded mozzarella over the top of the stuffed shells. Bake in a preheated oven at 350°F for 20 minutes, or until the cheese is melted and the edges are bubbling.