Bring a large pot of salted water to a boil. Add the broccoli and cook for about 2 minutes. Transfer it to a colander with a slotted spoon and rinse with cool water. Dice the cooked broccoli.
Add the jumbo shells to the boiling water and cook according to the package directions until al dente. Reserve 1/2 cup of pasta water, then drain the shells and rinse them gently with cool water.
Lightly spray an air-fryer-safe baking dish with cooking spray.
In a large bowl, combine the shredded chicken, ricotta, 1/2 cup mozzarella, Parmesan, egg, diced broccoli, 1/2 cup Alfredo sauce, salt, and black pepper.
Spread about 1/2 cup of the remaining Alfredo sauce over the bottom of the prepared baking dish.
Carefully fill each shell with about 1 tablespoon of the chicken mixture. Arrange the stuffed shells in the dish in a single layer.
Spoon the remaining Alfredo sauce over the shells and sprinkle with the remaining 1/2 cup mozzarella.
Place the dish in the air fryer. Cook at 310°F (155°C) for 5–10 minutes, or until the sauce is hot and the cheese is melted and bubbly.
Let the shells rest for a couple of minutes before serving. Finish with a little additional black pepper and fresh herbs if desired.